Ambassador Marcia Bernicat and her security team were unharmed but two cars belonging to her convoy were damaged. The incident took place amid protests for better road safety after two students were killed by a bus.
The protests began after two teenage students were run over and killed by a bus speeding down Dhaka's Airport Road on July 29. Since then, thousands of students have taken to the streets, with some even controlling traffic.
More than 100 people were injured in clashes with police in the Jigatala neighborhood on Saturday, with witnesses saying that officers had fired rubber bullets and tear gas at demonstrators.
They also reported that alleged pro-government activists had attacked protesting students.
The Awami League has denied allegations that its supporters had inflicted violence on the protesters.
Prime Minister Sheikh Hasina on Sunday urged the protesters to go home, and authorities have reportedly shut down mobile internet services in much of the country in an apparent bid to slow down protest mobilization and the spread of material that could cause further public outrage.
According to police, some 3,000 people are killed every year on Bangladesh's roads. But that figure is disputed by the private organization Bangladesh Commuters' Welfare Association, which says at least 7,397 people were killed in road accidents last year.
The protests over Bangladesh's transport regulations, which are widely seen as lax and corrupt, are also feeding into more general anger at the government's management of the country.
Recent months have also seen mass protests against a decades-old system of discriminatory civil service recruitment.