The 26-year-old German could miss the rest of the season due to a knee injury sustained in last week's friendly clash with Italy in Milan.
The 26-year-old suffered a torn anterior cruciate ligament after colliding with Andrea Pirlo in Germany's 1-1 draw with Italy last Friday and is now facing at least six months out of action.
There has been speculation that Khedira could even miss next summer's World Cup in Brazil but Alonso believes that his teammate will make a rapid recovery.
"Khedira’s injury came as a shock to us," Alonso told reporters at an Adidas event. "We were waiting to hear what had happened for a few hours because we weren’t sure how serious the injury was. After that, the worst was confirmed.
"However, he’s very German and very stubborn, so I’m sure he’ll be back sooner than expected. He was playing really well, very happy in his position, and this is terrible news."
Khedira has made 11 Liga appearances for Madrid this season, scoring once in the process.