Salah came off in tears half an hour into Liverpool's 3-1 defeat in Kiev on Saturday, having hurt his shoulder under a challenge from Ramos.
The 25-year-old has ligament damage in his shoulder, according to the Egyptian Football Association, amid initial fears the forward could be in doubt for the World Cup.
Ramos, who was slammed for the tackle, went on Twitter after the game, writing he hoped Salah could make a quick return.
"Sometimes football shows you it's good side and other times the bad," he wrote.
"Above all, we are fellow pros.
"Prompt recovery, Salah. The future awaits you."
Gareth Bale's brace led Madrid to a third successive Champions League crown and Ramos' fourth in total.
After the contest, Ramos also downplayed team-mate Cristiano Ronaldo's comments which suggested an exit for the star attacker, saying Ronaldo will find no better fit than at Real Madrid.