Shelvey grabbed the winner for Swansea in the 73rd minute, scoring from 25 meters to complete a league double for the Welsh side over United.
Five weeks after his big-money transfer to Manchester City, Wilfried Bony is ready to play his first match for the English champions.
Louis van Gaal has been warned as to his future conduct following comments he made about the referee.
Thorsten Stuckmann claimed on Wednesday that striker Rooney has apologised for his alleged "dive" during Manchester United's 3-1 win in FA Cup.
Gaal was rewarded for a bold change of tactics as his team came from behind to beat Preston North End 3-1 in the FA Cup fifth round on Monday.
United had to come from behind to avoid an upset at Preston, rallying with three second-half goals to beat the third-tier club 3-1 and reach the quarter-finals.
Wayne Rooney hasn't scored in 2015 and has picked up more yellow cards than goals in his last 13 games for Man United.
Van Gaal came under fresh attack on Friday over his style of play at Manchester United and acknowledged he was still struggling to come up with a preferred system.
United team looked laboured and uninspired in a 3-1 Premier League win over Burnley on Wednesday.
Chris Smalling scored twice after coming on as an early substitute to set Manchester United on their way to a 3-1 win over Burnley.
Diagrams showed United's passes went sideways or diagonally, rather than forward.