Twitter accounts of IS supporters posted a claim of responsibility identifying the attacker as a Tunisian.
Mohammed al-Shami, a spokesman for the Misrata-based Libya Dawn militia, said the attack today killed five people and wounded seven.
A local journalist, Taher Zarouq, said the attack caused extensive damage to the western Dafniya gate, a major commercial entrance into Misrata.
Libya is torn between several competing armed groups.
The local affiliate of the IS group has recently made territorial gains in central Libya, seizing the city of Sirte.
