The All India Football Federation's acting president Praful Patel made the appointment in accordance with the decision taken by the executive committee on Monday.
Mohun Bagan had suspended Bhutia in June for six months without pay after he missed team training and an exhibition match.
Bhutia made an appeal to the Indian Football Association (West Bengal body) but later the AIFF took up the matter. The national body's players' status committee, however, failed to decide on the matter as one member refused to give his opinion.
The AIFF then asked its outgoing general secretary Alberto Colaco to mediate between Mohun Bagan and Bhutia. Since Colaco also could not find a solution, the AIFF executive committee decided to refer the matter to an arbitrator.
"Both Mohun Bagan and Bhutia took a very firm view that they were right on the issue, so we cannot take a ruling. We will seek a legal solution now.
"We have decided to refer the matter to an arbitrator. The matter will be resolved in a week's time," Patel said after the executive meeting.
Dempo's AFC Cup tie may be shifted from Goa
Bhutia set to ink deal with East Bengal
SC extends ban on SIMI till October
AIFF suspends Paul
Bhutia to quit Mohun Bagan