Shakib retired hurt during Bangladesh innings against Ireland on Wednesday after scoring a half-century.
"Shakib sustained a left-sided back muscle spasm injury while batting during the match against Ireland," Bangladesh team physiotherapist Thihan Chandramohan said in a statement.
"He is undergoing assessment and treatment and we will make a decision regarding his availability for tomorrow's tri-series final on the morning of the match," he added.
Bangladesh won three out of their four games in the tri-series with one game against the hosts Ireland washed out.
A win in Friday's final against the West Indies would give Bangladesh their first trophy in a multi-team competition.