Mortaza fell awkwardly while bowling on the third day of the first test at St Vincent on Saturday, limped off the field without completing the over and did not return.
Captaining Bangladesh for the first time since replacing Mohammad Ashraful last month, Mortaza faces a race against time to be fit for the second test of the two-match series.
"He has damaged his left knee ligament and is unlikely to take any further part in the match, but the team physio is working hard to get him fit before the second test," BCB media manager Rabeed Imam told reporters.
"Nazmul will join the squad as cover, leaving on the first available flight."
Bangladesh are in sight of a rare test win against a West Indies side weakened by a mass boycott, the tourists leading by 252 runs with five wickets intact in their second innings heading into Monday's final day.
The second test will be held in Grenada from July 17 to 21, followed by three one-dayers and a Twenty20 international.
