Veran is one of several current or former ministers being probed over their response to the pandemic following complaints by victims of Covid-19 that they were slow to act to check its spread.
Veran's office was also searched as part of the investigation by a court that hears cases of alleged wrongdoing by ministers in the course of their duties.
Officers also searched the home of the director of the national health agency, Jerome Salomon.
Prime Minister Jean Castex is also under investigation over the pandemic, as is his predecessor Edouard Philippe and Veran's predecessor in the health ministry, Agnes Buzyn.
Critics accuse the government of being too slow to roll out large-scale Covid-19 testing and playing down the importance of wearing masks at the outset of the pandemic, when face coverings were in short supply and being reserved for health workers.
