The Holland midfielder got hurt in Sunday's Serie A match at Napoli and will undergo surgery later this week to repair a torn anterior cruciate ligament in his left knee.
Strootman will be sidelined for at least six months and will miss this summer's World Cup in Brazil.
A statement from Totti, on his official website, read: "Strength Kevin!
"All you have to do now is to think about your recovery.
"I know you will do so with the same determination that you show each time you go out on the pitch.
"We will wait for you and I can't wait to organise a dinner to celebrate your return."
The 37-year-old Totti overcome the same injury in the 2007-08 campaign.
Fabio Parisi, the Italian representative of Strootman, also believes his client will come back stronger than ever.
"I am in close contact with the agent of Strootman and I exchanged several text messages with him," Parisi said to asromanews.it. "The news has stunned everyone. Needless to say, we are very sorry.
"Injuries, however, are part of the game of football. You have to know how to draw a line and start from there.
"Strootman will see that and come back stronger than before. The determination that he has shown on the field is a reflection of his character.
"The fact that he tried to stay on the pitch at the Stadio San Paolo until the end is ample proof of this."
Strootman joined Roma last summer from PSV Eindhoven and has scored five goals in 24 league appearances for the Giallorossi this season.