Teemu Pukki will join Oliver Skipp on the sidelines for Norwich's last game of the season against Barnsley.
Top-scorer Pukki was sent for scans following the Canaries' 4-1 win against Reading at the weekend and they revealed ankle ligament damage.
On-loan midfielder Skipp has returned to Tottenham and undergone surgery on a fractured metatarsal in his right foot.
Finland expect Pukki will recover ahead of their Euro 2020 finals campaign, which starts against Denmark in Copenhagen on June 12.
The forward, 31, is scheduled to join up with his international team-mates at a pre-tournament training camp later this month.
A statement on the Football Association of Finland website read: "Teemu Pukki has suffered an ankle ligament injury, the recovery of which will takes some weeks in current estimates.
"The injury does not require surgical treatment, but rehabilitation will take time.
"Teemu Pukki will have to miss Norwich's last league match due to an ankle injury. He is scheduled to join, according to the Owls, when the team gathers for the preparatory camp in late May."
Finland head coach Markku Kanerva added: "We believe that Teemu will be fit to play at the European Championships.
"The treatment programme and recovery have already started and everyone is aiming for Teemu Pukki to be in full working order when the European Championships start."
