Robbie was named skipper by new boss Steve Staunton on Tuesday and Mido believes he is the right man for the job.
"It is a massive honour and I am very happy for him," said the Egyptian international. "I think Robbie deserves it because he has a great character suited to leadership, has a very good influence on the squad and in the dressing room.
"I think he is one of the most important players for us on and off the pitch - and the same for his national team.
"I congratulate him on this honour and hope he does the job well and the Republic get good results."
Fellow striker Mido has offered his congratulations to Robbie Keane on his appointment as captain of the Republic of Ireland.