Culture Secretary Oliver Dowden said at a news conference that Johnson was “wholly unscathed”.
The protester, who was knocked to the ground in the incident, was detained by police. The Metropolitan Police said he was arrested on suspicion of public order offences and for “obstructing the highway”.
Several groups were protesting outside Parliament in small numbers on Wednesday, including anti-Brexit and pro-Kurdish groups.
Johnson was returning to his office at 10 Downing St from his weekly question-and-answer session with politicians when the crash happened.