MS Dhoni failed to get India over the line during the world record chase of 246 between West Indies and India in Florida.
Misbah, who is asymptomatic, will now remain in quarantine in Jamaica for 10 days and will be allowed to return to Pakistan upon clearing subsequent Covid tests.
Pakistan have not lost a Test series to the West Indies in the last 21 years, with the Windies winning in 2000.
Shaheen Afridi picked up 6/51 and Pakistan held the advantage against West Indies in Jamaica.
Pakistan are on top after the end of day 3 of the second Jamaica Test against West Indies thanks to Fawad Alam's century.
Azam, who is also the Test skipper for Pakistan, played a captain's knock as he made 75 runs off 175 deliveries. He was exceptionally supported by Alam.
Jimmy Adams's 48, which did not include a single boundary, helped West Indies beat Pakistan by one wicket in the 2000 Antigua Test
Kemar Roach and Jayden Seales shared a 17-run stand for the final wicket, with Seales becoming the youngest to five wickets as West Indies won by one wicket.
West Indies managed to take a lead against Pakistan on the second day of the Jamaica Test.
Pakistan were boosted by a fifty from Fawad Alam and two late wickets by Mohammad Abbas.