The Three Lions boss made the annoucement during Thursday’s press conference with the 21-year-old struggling with an ankle issue, and has returned to Manchester United to begin treatment.
“He’s been with our medical team all week,” Southgate told reporters. “We’ve tried to progress his training through the week, so he did some running with them, but it’s clear to us he’s not going to be ready for our matches.
"We’re going to send him back to the club and he’s out of the two games.”
It means that Rashford will be unavailable for the start of England’s qualification campaign which begins on Friday when they host Czech Republic at Wembley.
The news will come as a blow for Southgate and his staff, as the Red Devils forward has developed into one of the squad’s most dependable players.
He has played in each of England’s last 11 matches and netted in both Nations League games against Spain in 2018.
Rashford has also been in superb form for the Red Devils in recent months and has scored six in his last 10 Premier League matches, as well as bagging the decisive penalty against Paris Saint-Germain in the Champions League last 16.
However, while Southgate will remain disappointed that he cannot turn to the striker, the Three Lions manager did admit Rashford’s absence presents opportunities for the likes of Jadon Sancho and Callum Hudson-Odoi.
“They've both been exceptional. They are ready. I won't hesitate to start either of them,” Southgate said of the two teenagers.
In particular, the 48-year-old has been impressed with Chelsea's Hudson-Odoi, who has earned his first call up to the senior team.
“He has the ability and mentality,” said Southgate. "Players have to have quality to play in the shirt. Ideally they play regularly but I can't wait for clubs to pick a player 100 times. If they're good enough, I pick them.
"Callum has looked every inch an England player in training.”