Clarke's side are on a three-match losing run, but only one of those defeats came last month - and that was on the back of four successive wins.
A home victory over Chelsea was particularly impressive, and West Brom remain sixth in the table in Clarke's first season in charge.
He told the club website: "It's a good reward for a good November. I'm the one that picks the award up but it's obviously down to the work of my staff and players. The players were exceptional in November."
Fellaini, meanwhile, has been honoured after scoring four times during a month which saw Everton beaten just once.
The Belgium international now has eight goals for the season.
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