The incident, which occurred as US Defence Secretary Jim Mattis was visiting the country, occurred near the site of a military parade.
"At 1406 (1206 GMT) we received information about an explosion of an unknown object," a police statement said.
"A man and a woman received bodily injuries," it said, adding that investigators and explosion experts were working at the scene on Grushevskogo street, near the building of the Ukrainian government.
Officials quickly cordoned off the area and the wounded individuals were taken away, an AFP correspondent said.