The Chelsea record goalscorer exacerbated an existing sore achilles tendon on the club's pre-season tour of Asia.
He'd been picked to start for the Blues during their first game of the tour, but dropped out after suffering a recurrence of the problem in the pre-match warm-up.
Mourinho said he'd put his players through '14 training sessions of intensity' as the new Chelsea boss looks to prepare his side for a Premier League title challenge next season.
They have a rest day travelling from Bangkok to Kuala Lumpur before facing a Malaysia XI at the weekend.
Mourinho will put his team through a double training session on Friday prior to Sunday's friendly, but the report claims the ex-Real Madrid boss has ordered Lampard not to take any risks.
The Stamford Bridge side don't think his injury is a long-term concern, but they do not want to push the 35-year-old midfielder too hard.
"It is a precaution," Mourinho told the Daily Mail. "I always say the players have to be intelligent in this period. No risks if they feel a little thing.
"In competition you have to risk something. In pre-season, the worst thing that can happen is an injury while taking a risk.
"He was feeling discomfort on his achilles, so we decided he wouldn't play. Ramires is a natural runner so it wasn't a drama for him to play 90 minutes. Frank will rest and in two days’ time he'll be back in training."