The midfielder, who had already been booked, escaped punishment for his challenge on Barnes in the second half at the King Power Stadium on Sunday as United held on for a 1-0 victory after Marcus Rashford's early goal.
Sources have told ESPN FC that referee Mike Dean saw the incident at the time and the FA will not review the footage, leaving Matic free to face Fulham at Craven Cottage on Saturday.
The United squad were given the day off on Monday before preparations begin for a tough run of six games in 22 days. They play Fulham in the Premier League on Saturday before Paris Saint-Germain visit Old Trafford for the first leg of the Champions League round of 16 tie next Tuesday.
United then face back-to-back games against Chelsea in the FA Cup and table-toppers Liverpool in the league before a trip to Crystal Palace on Feb. 27 and a home game against Southampton on March 2.