Forest top the table after going unbeaten in their opening five games of the season, winning the first four.
Although they were knocked out of the Carling Cup after fielding an under-strength team at Accrington Stanley, Calderwood still took the prize.
Port Vale boss Martin Foyle and Brentford's Leroy Rosenior were also in the running.
Swindon boss Dennis Wise was named League Two manager of the month, with Cardiff chief Dave Jones taking the honours in the Championship.