The diplomat was arrested in the early hours of morning after being caught speeding in his Mercedes close to the Sorbonne university.
Even after his tyre was shot out, the diplomat briefly continued trying to escape the police car pursuing him and he was subsequently found to be over the drink driving limit, the police source said.
The ambassador, Stefan Flückiger, was released from custody after police confirmed his diplomatic status but he may now face prosecution.
A spokesman for Swiss Foreign Affairs Minister Didier Burkhalter said Flückiger would remain as ambassador for the moment.
"We should first of all let the justice system do its work," Jean-Marc Crevoisier is quoted as saying by Le Matin.
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The ambassador "will be judged like an ordinary driver," Crevoisier said, adding that the department of foreign affairs had agreed to lift Flückiger's diplomatic immunity.