Ten Arsenal players in the past week either did not join their national team or left camp early as coach Mikel Arteta's team chases three trophies, including a first English title in 22 years.
"The risk for making it worse was just way too big," Tuchel said of fitness assessments for Rice and Saka ahead of hosting Japan on Tuesday in a World Cup warm-up game.
Midfielder Rice and winger Saka are likely starters for England at the World Cup and also key to Arsenal's quest for a first EPL title under Arteta after three straight runner-up finishes.
"They were both clearly in discomfort when we did the medical assessment, so it made absolutely no sense that they stayed," said Tuchel, adding that both "wanted desperately to be involved."
Other Arsenal players who left national-team camps over the weekend after playing include Spain midfielder Martin Zubimendi and Ecuador defender Piero Hincapié.
Central defenders William Saliba and Gabriel Magalhães did not travel with France and Brazil, respectively, for those teams' warmup game in the United States last Friday. France won 2-1.
Arsenal's intense April schedule starts on Saturday with an FA Cup quarter-final at Southampton. They play at Sporting Lisbon three days later in a Champions League quarter-final first leg.
Arsenal have seven games left in the EPL, and sit nine points ahead of Manchester City who have a game extra to play. Arsenal's next EPL game is at home against Bournemouth on April 11.
The following weekend they travel to main rivals Manchester City, who beat them 2-0 in the recent Carabao Cup final at Wembley.
Two Arsenal players will be involved in World Cup qualifying play-offs on Tuesday. Viktor Gyökeres leads Sweden's attack against Poland, days after his hat-trick in a 3-1 win over Ukraine, and defender Riccardo Calafiori's Italy faces Bosnia-Herzegovina away.
