Police described the device as a remotely controlled fragmentation mine.
The bomb is commonly used by separatist Liberation Tigers of Tamil Eelam (LTTE).
The group has not claimed responsibility for the assassination.
Dassanayake was not a member of the cabinet and represented the United People's Freedom Alliance party.
Hours after the roadside bombing, a second explosion went off in the heart of Colombo, police and local residents said on Tuesday night.
Police said they suspected the later bomb may have targeted a prominent individual travelling near the Colombo Fort area, a high security zone.
There were no immediate details of casualties.
The government announced last week it was ending a ceasefire with the LTTE, that has largely been ignored in recent months.
The truce was signed in 2002 and brokered by a team of Norwegian negotiators.
Paikiasothy Saravanamuttu, a political analyst with the Centre for Policy Alternatives in Colombo, told Al Jazeera that the assassination was not specific to Dassanayake.
"It is an open season in terms for tit-for-tat killings of high-ranking officials from both sides. The fighting is going to intensify and we are going to have these assassinations and counter assassinations."
Saravanamuttu said the ceasefire agreement was not being observed on the ground.
"The government has said it is going to eliminate the LTTE as an organisation by August of this year. In terms of the ethnic conflict, we have to come out with a political proposal."