Why did the United States not invade North Vietnam?

The sole reason was fear of Chinese intervention just like in Korea.

Chinese were fully committed to the war. Mao allegedly said:

Best turn it into a bigger war. I’m afraid you really ought to send more troops to the South. Don’t be afraid of U.S. intervention, at most it’s no worse than having another Korean War. The Chinese army is prepared, and if America takes the risk of attacking North Vietnam, the Chinese army will march in at once. Our troops want a war now.

_{What is happening to America? The hidden truth to global Destruction - Simona Pipko ¹}

What was worse, Chinese and Soviets allied against US (Of course later they split up) as Richard Halbrooke said:

2,000 years of Chinese-Vietnamese enmity and hundreds of years of Chinese and Russian mutual suspicions were suspended when they united against us in Vietnam.

China had already sent military and financial aid to North Vietnam in billions. Chinese servicemen sent to North Vietnam for rebuilding and aerial defense numbered to almost 170,000. As Mao said to premier Dong:

Why have the Americans not made a fuss about the fact that more than 100,000 Chinese troops help you building the railways, roads and airports although they knew about it?

_{Vietnam: The necessary war - Michael Lind ²}

The answer to why the Americans did not make a fuss about it was that they were afraid of further escalating the tensions with the Chinese to an all-out war. Wikipedia article on President Johnson also confirms it as:

Johnson was afraid that if he tried to defeat the North Vietnamese regime with an invasion of North Vietnam, rather than simply try to protect South Vietnam, he might provoke the Chinese to stage a full-scale military intervention similar to their intervention in 1950 during the Korean War, as well as provoke the Soviets into launching a full-scale military invasion of western Europe.

In any case, China was not ready to allow Vietnam become the third bastion of the Western Capitalism, like South Korea and Taiwan, to threaten/encircle her and therefore was willing to go through with any action to halt that course.

From Semaphore's excellent answer to Why China did not assist in Vietnam like they did in Korea:

[I]f the Americans went beyond the bombing of the North and used ground forces to invade North Vietnam, China would have to send military fores. Second, China would give clear warning to the Americans.

_{- Harper, John Lamberton. The Cold War. Oxford University Press, 2011.}

Americans feared the outcome if they crossed the border into North Vietnam.

The near-certainty of a second war with China deterred the Americans from taking the ground war beyond the 17th parallel.

- Harper, John Lamberton. The Cold War. Oxford University Press, 2011.

And also

General Dave Richard Palmer writes: The Johnson administration had already barricaded the one sure route to victory - to take the strategic offensive against the source of the war. Memories of Mao Tse-tun's reaction when North Korea was overrun by United Nation troops in 1950 haunted the White House ... Summers contends that the US was "bluffed" by China.

^{Hess, Gary R.Vietnam: Explaining America's Lost War}

So Americans decided not to take the war to North Vietnam on ground because of fears of Chinese intervention.

Whether Peking's threats were genuine or not, American presidents prudently refused to risk such high odds. North Vietnam remained inviolable to ground attack.

^{McNeill, Ian, and Ashley Ekins. On the Offensive: The Australian Army in the Vietnam War, January 1967-June 1968. Allen & Unwin, 2003.}

^{1.Treat Simona Pipko as an unreliable source because of her biased views against Left Wing politics. But she is the only source I could find for this quote. Those who might have an issue viewing Google books for this entry can see it here.}

^{2. Those who can't view Google Books entry for Michael Lind's book, please refer to this screenshot.}