Shakib was in visible pain Wednesday during the 36th over of the Bangladesh innings against and briefly continued his batting before retiring hurt with a half-century off 51 balls.
Bangladesh later won the match against the hosts by six wickets.
"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 all three of their matches in the tri-series comfortably to set up a final against West Indies with one game against Ireland rained off.
A win Friday would give Bangladesh their first trophy in a multi-team tournament.
The tri-series in Ireland was organised as part of the teams' build-up for the World Cup, starting on May 30 in Britain.
Bangladesh will begin their campaign in the World Cup against South Africa at the Oval on June 2.