The England international was forced off the pitch in his side's 2-1 defeat at the hands of Huddersfield Town on Saturday. He was replaced by summer signing Victor Lindelof, whose error allowed David Wagner's side to take a 2-0 lead after the first half.
According to the Manchester Evening News, Jones was flown with the squad and his inclusion for the trip to face Swansea will come as a welcome boost for United's next league tie against Tottenham Hotspur at Old Trafford. The centre-back and Eric Bailly have been a rock in the heart of the Red Devils' back four.
Earlier reports suggested the Ivory Coast international could return to action against Paul Clement's side. However, Bailly, who has been sidelined since the last international break, has not travelled with the squad.
Bailly joins goalkeeper David de Gea and right-back Antonio Valencia to miss the trip to Wales. The trio joins injured players Zlatan Ibrahimovic, Marcos Rojo, Paul Pogba, Michael Carrick and Marouane Fellaini to miss the clash against the Swans.
Luke Shaw has travelled with the squad and the left-back could be in contention for his first start of the season. He has made only one appearance for the 20-time English champions in all competitions this season, when he came on as a substitute against Burton Albion.
Matteo Darmian and Ashley Young are the other full-back options, with the former likely to start on the right side of the back four. Romelu Lukaku was on the bench against Burton and the Belgium international is likely to settle for a place on the bench against Swansea on Tuesday.
The full squad as reported by the Manchester Evening News is given below:
Sergio Romero, Joel Pereira, Kieran O'Hara, Daley Blind, Chris Smalling, Victor Lindelof, Axel Tuanzebe, Phil Jones, Matteo Darmian, Luke Shaw, Ashley Young, Nemanja Matic, Jesse Lingard, Scott McTominay, Ander Herrera, Juan Mata, Henrikh Mkhitaryan, Marcus Rashford, Romelu Lukaku, Anthony Martial.