A crescendo of boos from the home supporters had greeted the final whistle, while jubilant United fans celebrated their team rising to ninth in the table in manager Simon Grayson's 100th match in charge.
Those detained were arrested on suspicion of committing assault, public order and drunk and disorderly offences.
Of the 23 arrested, six are understood to have been Leeds supporters and 17 home team fans. It is not yet known how many of the total have been charged with offences.
In the past police at Middlesbrough have held back groups of supporters to avoid trouble, but on some occasions a group have shown a determination not to be held back, said spokeswoman for Cleveland Police.
On this occasion it was judged to be safer to allow both groups of fans to leave the ground together to avoid risk of crushing problems.