The former Juventus and Chelsea manager saw red after 90 minutes in the goalless draw, believing referee Fabio Maresca had not added on enough stoppage time.
The Lega Serie A punished Conte for "disrespectful phrases towards the referee that continued off the pitch".
"In the tunnel that leads to the changing rooms (Conte) confronted the referee in a threatening manner, screaming at him a seriously offensive expression," Lega Serie A side in a statement.
Inter team technical manager Gabriele Oriali was also fined 5,000 euros, and given a one-match ban.
Inter missed the chance to move level on points with leaders AC Milan.
Conte will miss their next two league games against Benevento and Fiorentina.
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