Donny van de Beek was handed his first European start and Paul Pogba returned to the side after being named as a substitute for United's last three games.
Scott McTominay joined Fernandes and Rashford on the bench and Solskjaer said that the congested fixture schedule had forced him to make changes.
"Bruno and Marcus have played the last five, three for us and two internationals," he said.
"Scott played the last three plus three internationals. So five games in 14 days, six games in 17 for Scotty. You've got to look after the players."
"We have to cause them [Leipzig] more problems than they can cause us. Iâve picked a team we think can win the game and cause problems. Iâll always pick a team I think can win the game."
Solskjaer makes a total of four changes from Saturdayâs 0-0 draw with Chelsea, as Mason Greenwood and Nemanja Matic join Pogba and Van de Beek in the line-up.
Edinson Cavani, who made his United debut as a substitute against Chelsea, is once again named on the bench.
Manchester United: De Gea; Wan-Bissaka, Maguire, Lindelof, Shaw; Matic, Pogba, Fred, Van de Beek; Greenwood, Martial.
Substitutes: Henderson, Cavani, Mata, Rashford, Fernandes, James, Fosu-Mensah, Ighalo, Williams, Tuanzebe, McTominay, Mengi
RB Leipzig: Gulacsi; Konate, Upamecano, Halstenberg; Henrichs, Nkunku, Kampl, Angelino; Olmo, Poulsen, Forsberg.
Substitutes: Tschauner, Martinez, Orban, SAbitzer, Hwang, Adams, Sorloth, Samardzic, Kluivert, Borskowski, Martel, Wosz.