Nitul Gogoi, Dispur's superintendent of police, told Reuters: "We are yet to confirm the details of the blast, but preliminary investigation points to the handiwork of the ULFA."
Gogoi said the bomb was placed in a busy vegetable market, near the state assembly and some of the injured included vendors and customers.
Earlier in the day, two civilians were wounded when suspected rebels attacked a military convoy in front of a state government guest house in Goalpara, about 100km west of Guwahati, Assam's main city.
Singh visited the state on Tuesday, which has substantial resources of oil and tea, to meet families of more than 70 people who authorities say were killed by ULFA guerrillas earlier this month.
Singh said the government was willing to talk to the rebels, provided they reject violence.
The conflict - which ULFA says is aimed at gaining Assam's independence from India - has killed more than 20,000 people since it began in 1979.