Ramsey, who featured in only 19 of Wales’ previous 44 games before playing at Euro 2020 this summer, suffered a thigh injury playing for his Italian club on August 22.
Liverpool full-back Neco Williams, Tottenham defender Joe Rodon and QPR midfielder George Thomas have also withdrawn from Wales duty through injury.
Brandon Cooper, Mark Harris, Josh Sheehan and Ben Woodburn have been drafted into the squad.
But Swansea defender Cooper, alongside Chelsea midfielder Ethan Ampadu and Leeds striker Tyler Roberts, will miss the Belarus qualifier which has been switched to the Russian city of Kazan.
The trio were unable to get their Russian visa approved in time and will travel back to Cardiff after Wednesday’s friendly in Finland to prepare for the Estonia game, while the rest of the squad head to Kazan.
UEFA had to move the September 5 qualifier to a neutral venue with teams from the UK and the European Union unable to enter Belarus by air due to sanctions against the Minsk government.
Wales boss Robert Page, who continues to stand in for absent manager Ryan Giggs, has called the decision to play the game in Kazan – Russia’s fifth largest city 700 kilometres east of Moscow – “crazy”.
“Organising it from a financial and logistical point of view is a nightmare,” Page said after announcing a 27-man squad last week.
“The players will only be aware of it because of the bio-mechanic tests that we’ve got to do.
“We’ve got to get them organised to go to different parts of the UK to get their fingerprints done and get tested.
“We’ve had to pick a larger squad because of the visas, they’ve to be submitted three weeks before we go – which again is crazy.
“UEFA could have picked any neutral venue but they’ve decided on Kazan.”