The 25-year-old Adler will undergo rib surgery and Rolfes, his Bayer Leverkusen team-mate, has failed to recover from a knee injury which has kept him out of action for three months.
GEAR:Check out Germany's World Cup shirt
Adler became Germany's first-choice keeper after Robert Enke committed suicide last year and he has won nine caps.
"This was the most difficult decision of my life," Adler said in a statement. "But it would have been irresponsible for me, my club and the national team, to take part in the World Cup."
"Medically it was possible but the pain is so strong that I would not be able to be in top shape for training or the matches."
Werder Bremen's Tim Wiese and Schalke 04's Manuel Neuer, who have made two international appearances each, should be in the preliminary squad named on Thursday.
Borussia Dortmund's Roman Weidenfeller is among the candidates along with experienced Bayern Munich player Hans-Jorg Butt.
"We were informed of (Alder's planned operation) this morning and we are naturally very sad that Rene has to undergo surgery and will miss the World Cup," Low said.
"We will now sit down with the coaching staff to discuss which keeper will travel to South Africa and will announce it on Thursday."
"I am very satisfied with the healing process but it is clear from the schedule that it would make no sense to take part in the World Cup," said Rolfes, who has 21 international caps.
"My plan is now to be fully fit for the start of the new Bundesliga season. The decision to pull out did not come easy. Now there is nothing left but to wish the team success in South Africa."
"We are sad that he had to pull out but wish him a speedy recovery," Low said.
