The Israeli Defence Force said the target was a car carrying four members of the al-Aqsa Martyrs' Brigades, the group linked to the Fatah movement of Mahmoud Abbas, the president.
Witnesses said one of the activists was wounded and taken to a hospital. The other wounded person was a bystander.
Some witnesses said the explosion, in the early hours of Monday, was not powerful and left only a small hole in the street and hardly damaged the car. They said a similar small blast occurred a few streets away at about the same time.
Other witnesses said one of the two missiles failed to explode.
The military said the missiles missed their target.
The Israeli air force has frequently killed resistance fighters in Gaza in missile attacks, aiming for cells they say are responsible for almost daily rocket barrages from Gaza into Israel.
The Israeli occupation forces made no immediate comment.