Thol Thirumavalavan, a legislator from the southern Indian state of Tamil Nadu, and two of his associates were denied entry at the island's international airport, immigration controller Chula Perera said.
"When they were questioned at the immigration counter they were not clear about their visit," Perera said.
Thirumavalavan told the Chennai-based Hindu newspaper that they had wanted to attend Tuesday's cremation of Prabhakaran's mother, Vallipuram Parvathi, 81. Prabhakaran was killed by government forces in May 2009.
"I asked them what the reason to send me back was," Thirumavalavan told the Hindu. "But there was no satisfactory reply."
Sri Lanka's minority Tamils share close cultural and religious links with Tamil Nadu.
Prabhakaran's mother died in hospital on Sunday following a stroke last year.
The rebel leader's parents were captured by the military in the final stages of fighting between government troops and the Tamil Tigers in 2009.
His father died in military custody last year.