He said one of the blasts was outside a university campus and another was at a bus stand in a busy part of the city centre.
The last reported bomb attack in Kathmandu was at a police post in April 2006, just before the former rebel Maoists entered a landmark peace deal with the government after a decade of war against the monarchy.
Political parties formed a new government in April 2006 marking the end of 14 months of King Gyanendra's direct rule.
The rebels and the new government reached a pact in November that paved the way for the Maoists to join parliament in early 2007.
Both parties have pledged to campaign in polls scheduled for late November to elect a constituent assembly and rewrite the constitution, including the role of the monarchy.