"Liverpool Football Club can confirm Sadio Mane today underwent a procedure on a hand injury sustained while on international duty with Senegal," Liverpool said.
"The surgery, conducted at a north-west hospital and supervised by club medics, was successful. Mane's recovery will be monitored over the next couple of days."
Liverpool midfielder Naby Keita went off with a suspected muscle strain in Guinea's 1-1 draw against Rwanda on Tuesday while forward Mohamed Salah had to be taken off with a groin injury when Egypt beat eSwatini 4-1 in Cairo on Friday.
Defender Virgil van Dijk was withdrawn from the Netherlands squad for Tuesday's 1-1 friendly draw with Belgium as he was still feeling the effects of a rib injury that he suffered when playing for the club against Southampton last month.
Third-placed Liverpool will look to extend their unbeaten start to the league season at Huddersfield. Juergen Klopp's side entertain Red Star Belgrade in the Champions League next week.
(Reporting by Nivedita Balu in Bengaluru, editing by Ed Osmond)
