Were there historical examples of "citizen's arrest" concept in history independent of British common law?

This is a citation from the Criminal Code of the RussianSFSR of 1960 (original edition, without amendments):

Article 13. Necessary defense

Shall not be considered a crime any act, even having features of doing listed in the Special part of this Code, but conducted in the state of necessary defense that is when protecting interests of the Soviet state, public interest, personality or the rights of the defending or another person from an offense dangerous to the public by causation of damage to the offender, if when doing so there was no commited infringement upon the limits of necessary defense.

Infringement upon the limits of necessary defense shall be considered evident inconsistency of defense to the character and danger of the offense.

Article 14. Extreme necessity

Shall not be considered a crime any act, even having features of doing listed in the Special part of this Code, but conducted in the state of extreme necessity that is for neutralizing of danger threatening the interests of the Soviet state, public interest, personality or the rights of the person or other citizens if this danger under given circunstances could not be neutralized by other means and if the caused damage is less substantial than the prevented damage.

As you can see, these articles are more broad than just arresting somebody. As part of these articles you could catch any person if that would be necessary to prevent any further crimes.

Modern Russian criminal code mentions the right to catch an offender for delivering him to the police explicitely.

The concept of a non-citzen arrest is rather new.

Other than a medieval city watch which was really just to keep strangers out rather than to investigate crimes an official force to catch people is a new invention. General the state only got involved with constables and magistrates to prosecute offenders caught by the victim or his neighbours. In medieval Britain the whole village would be prosecuted if a criminal wasn't caught and handed over by the other townsmen.

Britain actively resisted any sort of official police because in those countries which did have one in the 19C it was seen as largely a political force to keep an eye on potential revolutionaries. The army was generally used for large scale policing.

Robert Peel had to go to a lot of effort to create a police force that didn't appear military and didn't essentially have any more power than a normal citizen. This is where the citizen arrest term came from - it was an attempt to prove that really these men in uniform were only doing what any citizen had the right to do.

There is a certain anachronism in your question to be assuming even the idea of "arrest" existed across time and space. In England there were no police until 1829, and even then it was only established in London (the "bobbies" created by the Metropolitan Police Act of 1829). Before this there were only the Bow Street Runners, who were a private group of less than 10 men (only 6 at the beginning) who had no special legal authority and worked for whoever paid them.

The normal mode of arrest in British law has always been by writ (or "warrant" in modern terminology) which must be produced by indictment before a justice of the peace, meaning a judge. In which case a bailiff or sheriff may then go, writ in hand, and arrest the person.

The law also provided that any person may kill another who attacks him with an intent to rob or kill, and may further arrest and imprison any malefactor who is observed in the commission of a felony, so long as he delivers the person to a justice of the peace or common jail expeditiously. This can be read in the Placiti Coronae (Pleas of the Crown at the King's bench). To quote from the commentary on these pleas by Hale (1778):

If A. a meer private man knows B. to have committed a felony, he may thereupon arrest him of felony, and he is lawfully in the custody of A. till he be discharged of him by delivering him to the constable or common gaol; and therefore if he voluntarily suffers him to escape out of his custody, tho he were no officer, nor B. indicted, it is felony in A.

It should be noted that historically most bailiffs were private persons anyway and the only thing that distinguished them was possession of a writ of arrest.

Other countries generally always have had similar laws. For example, in pre-Meiji Japan the law was that a person could not arrest another, but you could demand a person's name and insist they report to the nearest police station to answer for a crime. In such cases YOU (the accuser) had to go to the police station immediately as well. To fail to answer such an accusation meant death. Note that you could only arrest a peer in this way. A commoner, for example, could not demand the name of a samurai. If a person was an outlaw in Japan, anybody could kill them freely.

The general pattern in Europe follows the Roman principle venices injuriam, the vengeance of the injured, which allows anyone who is harmed, or even a witness, to raise hue and cry and arrest the perpetrator. For example, in the Republic of Venice anybody could arrest a criminal on the fly. Quoting from Lithgow (1770):

[at Canea]...a young French gentleman, a Protestant, born near Montpellier in Languedock; who being by chance in company with other four of his countrymen in Venice, one of them killed a young noble Venetian, about the quarrel of a courtesan whereupon they flying to the French ambassador's house, the rest escaped, and he only apprehended by a fall in his flight, was afterward condemned by the senators to the galleys during life.

In Islamic Sharia law all people are obliged to enforce the statutes, so perforce, citizen arrests are permitted.