During United's 1-0 defeat at Bristol City last month, Monk was sent to the stands by referee Keith Stroud following an 88th-minute outburst.
The ban will be served during Saturday's Sky Bet Championship trip to Derby.
Huddersfield boss David Wagner has received the same fine - but no ban - after he also accepted a misconduct charge, the FA announced on its official Twitter account
The governing body considered his behaviour at the end of Town's recent 1-0 defeat at Reading to have amounted to improper conduct
Huddersfield saw midfielder Rajiv van La Parra sent off in that match and four other players booked
Source : PA
Source: PA