Tebboune, 75, has been in office for less than a year after winning an election to replace the veteran president Abdelaziz Bouteflika, who was ousted during mass protests last year.
He said on Saturday he was self isolating after senior government aides had fallen sick and on Tuesday state media said he had been admitted to a specialised treatment unit in an army hospital, without saying if he had COVID-19.
"I assure you, my brothers and sisters, that I am well and healthy and that I continue my work," he was quoted as saying on Saturday, and Tuesday's statement said he was still working.
Algerian leaders have historically sought treatment in Europe for more serious medical problems.
Tebboune's departure for Germany comes days before Algerians vote in a referendum on Sunday on changes to the constitution that Tebboune has pushed as part of the government's efforts to turn a page on popular unrest.
(Reporting by Hamid Ould Ahmed and Lamine Chikhi, additional reporting by Alaa Swilam; editing by Angus McDowall and Emelia Sithole-Matarise)
epa08770336 (FILE) - Algerian President-elect Abdelmadjid Tebboune speaks during a press conference in Algiers, Algeria, 13 December 2019 (reissued 24 October 2020). According to a presidency press release, Algerian President Abdelmadjid Tebboune will start a five-day voluntary quarantine as per medical staff of the presidency advice after senior officials showed symptoms of Coronavirus infection. EPA-EFE/MOHAMED MESSARA 