First secretary Alexander Vitisov has 24 hours to leave Doha, a Foreign Ministry spokesman told the official Qatar News Agency on Wednesday.
Moscow was notified on Tuesday of the move.
"I was expecting something like this, but I've not received anything official yet," said Moscow's ambassador Victor Koudryavtsev. "This person will leave if it is Qatar's decision."
He did not reveal what sparked the expulsion notice.
The announcement came shortly after the return home of two Qatari nationals, who were detained in Moscow after two Russian security agents were charged with assassinating former Chechen President Salim Khan Yandarbiyev in Doha last month.