Were there any abolitionists imprisoned for being critical of the Congress or the President during the American Civil War?

I presume you are talking about the North, during the war itself.

The newspapers shut down in those cases were invariably Copperhead newspapers that opposed the war, not slavery.

It is true many abolitionists criticized Lincoln, but they were not arrested. For example, according to the "Report and Evidence of the Committee on Arbitrary Arrests in the State of Indiana" (1863):

No Abolitionist who thus indulged in denunciations of the policy of the conduct of the war was arrested, but the least offense in that respect by a Democrat was met by the stern hand of power.

It seems very unlikely. Why would Lincoln arrest men who, even if critical of the government, were even more critical of the slave states? My TLDR is that the majority of the arrests were of Southerners or Border Staters who, in some way, materially supported the Confederacy. The pattern of the arrests is entirely inconsistent with arrests for mere political dissent, especially the type of dissent that a radical abolitionist might perform.

Now for the details: One analysis of arbitrary arrests during this period shows that they were overwhelmingly concentrated in slave states, especially Maryland:

The most notable feature of the arrests is their geographic distribution. Of the 866 persons on the list, place of residence is noted for 582. One hundred and seventy-one were Marylanders. Thus a state with a little over 3 percent of the North's population produced 29.4 percent of the persons arrested by the Lincoln administration in the first year of the war.

A near equal percentage of the arrests were of citizens of Confederate states:

Another substantial percentage of persons arrested were not Northerners at all. Seventy-nine of the 582, or 13.6 percent were Virginia residents, and another 12.7 percent were residents of other seceded states. Thus a whopping 26.3 percent of the people arrested were citizens of Confederate states, either persons arrested for causing trouble in the few areas of the South controlled by Union armies in the first year of the war or Southerners trapped in the North when the war began and arrested for trying to get back home to join the Confederacy.

Geography aside, many arrests had nothing to do with political dissent:

Examining the reasons for the arrests gives further cause to appreciate their lack of impact on Lincoln's political fortunes and helps provide some measure of their efficiency. Among the 866 arrests known to have occurred under Seward, 612 have some notation of cause of the arrest. Many of them have nothing to do with political dissent — or any other activity which normally takes place on dry land. One hundred and fourteen (or 18.6 percent) were picked up in boats or immediately upon disembarking from a vessel.

What were they arrested for? Materially supporting the Confederacy:

It should be remembered too that many of the arrests involved allegations, not of victimless crimes like holding the wrong political ideas, but of serious ones like murdering pickets, bushwhacking, burning bridges, and raising money and men for the Confederate Army. This was especially the case in Missouri, Virginia, and Kentucky (always) and Maryland (at times of invasions of the North). The likelihood, of course, is that the percentage of serious crimes rose after 1862 as the Union conquered more and more Southern territory, just as it is likely that the percentage of the civilians arrested who were Confederate citizens and not possible voters for or against Lincoln rose.

The linked study does not mention any abolitionists. It's hard to prove a negative, but unless someone can find an example of an abolitionist who was arrested, I think it is very unlikely.