Brough was cited for a tackle on Wakefield utility back Reece Lyne in the 14th minute of Giants' Challenge Cup defeat by the Wildcats on 23 May.
The 33-year-old will now miss his side's Super League game against leaders Hull FC on Thursday.
Huddersfield are 11th in the table, six points outside the top eight places.
Huddersfield Giants half-back Danny Brough has been banned for one game after submitting an early guilty plea to a Grade B high tackle charge.