Enslin is a 16-year veteran of SAP and was previously chief operating officer of SAP North America.
Tomb will return to the company in an as-yet-unspecified role, and his departure is unrelated to the company's business performance, SAP spokesman Saswato Das said.
Das could not say how long Tomb would be gone. He has been at SAP more than 12 years but was appointed to the CEO position only last year.
Earlier Wednesday, SAP had posted overall strong year-end results, but said it planned to trim its workforce by about 3,000 jobs and institute a wage freeze. Company executives had made no mention of Tomb's status during an earnings conference call.