The attack comes in the run-up to a local election for which TMVP has fielded candidates.
TMVP, founded by a rebel commander of the Liberation Tigers of Tamil Eelam (LTTE), is seen as an ally of the Sri Lankan government.
While investigations were being conducted, security forces sealed off all entry and exit points to Colombo, paralysing the country's capital city of 650,000 inhabitants.
NK Illangakoon, a police spokesman, said the force was awaiting a report from a government analyst to figure out if the bomb was triggered by a remote control or a timing device.
He said police had intensified awareness programmes to show bus and train commuters how to respond to a bomb threat.
The motorcycle attack came a day after a bomb suspected to have been planted by the LTTE destroyed a passenger bus on the outskirts of Colombo, wounding 18 people.
The vehicle had been evacuated beforehand and there were no fatalities.
Fighting between the military and the LTTE has escalated since the government formally pulled out of a six-year-old ceasefire pact signed in January.
Mahinda Rajapaksa, the president, argues that the LTTE used the truce to rearm themselves and were not sincere about peace negotiations.
The LTTE has fought for over three decades for an independent homeland in the Sinhalese-majority island.