The midfielder, on loan from Barcelona at Turkish Super Lig side Istanbul Basaksehir until 2020, was furious at a decision made by the assistant during Friday's 1-1 draw with Sivasspor.
Basaksehir had taken the lead but goalkeeper Volkan Babacan's own goal brought Sivasspor level in the second minute of injury time.
With his side, who are locked in a four-way fight for the title, chasing a vital winner, Arda - who came on as a substitute - broke clear down the right but was tackled, the assistant giving no foul.
An irate Arda shoved the official in the chest and was quickly dismissed by the referee, with a 16-match ban the punishment handed out to the 31-year-old as a result.
The suspension means Arda will miss a large chunk of the 2018-19 season as well as the conclusion of this term.
Basaksehir, three points behind leaders Galatasaray in third with two games remaining, are aiming to win the Turkish title for the first time.