Rajapaksa, in recent speeches, has repeatedly called on the Tigers to surrender, saying that if not they would be crushed.
"From today it's possible for us to prosecute people and organisations who contribute money or material to the Tigers," a government official said.
The announcement of the ban came as a blast on a railway track in a southern suburb of Colombo halted train services.
Police said there were no casualties in the minor explosion which damaged the track and was believed to be the work of the Tigers.
The government has warned that the rebels could launch terrorist attacks in the south as they face defeat in their northern strongholds.
The army has pushed deep into rebel-held territory and last week captured Kilinochchi, a northern Tiger stronghold.