Netherlands international Strootman had been enjoying a fine debut campaign at Stadio Olimpico, before he tore his anterior cruciate knee ligament in the 1-0 defeat to Napoli on March 9.
Strootman will now miss the rest of the campaign, while his hopes of featuring at the FIFA World Cup in Brazil later this year are almost certainly over.
Totti himself had been on the sidelines for the past month with a gluteal injury, but the veteran forward returned to score in Roma's 3-2 home win over Udinese on Monday.
The 37-year-old celebrated the win by waving Strootman's number six jersey in tribute to the former PSV midfielder.
"It's as if he were here." Totti told Sky Sport Italia. "He is a fundamental player and above all a great guy who settled in straight away.
"He's part of this group and I hope he can recover as soon as possible. He'll certainly be back stronger than ever."
Totti spoke of his own disappointment about his recent injury lay-off, but was thrilled to grab a crucial three points against Udinese, a result that boosts Roma's chances of holding off Napoli in the race for second place in Serie A.
He added: "Not playing hurt, but the important thing was to win and maintain the pace. We have Napoli biting at our heels, but we got the crucial victory."
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