The Sif actress was involved in an accident while filming in London.
"Today I sustained a pretty horrible injury," Alexander tweeted. "I'm lucky I'm not paralysed. Thank you (with all of my heart) to those who've looked after me.
"Already in recovery mode and my spirits are high. I'll be back kicking ass as Lady Sif in no time! It can only get better from here on out."
On Tuesday night (September 25), she wrote: "Received great news today! Meds are kicking in. Awesome funny nurses here at the hospital. Physio tomorrow. All good."
Alexander will reprise her role as the warrior goddess in the sequel to Kenneth Branagh's 2011 Marvel Studios film.
Filming on Thor 2 began earlier this month, with Chris Hemsworth, Tom Hiddleston and Anthony Hopkins also returning for the follow-up.
Thor: The Dark World is scheduled for release on November 8, 2013.
Photo gallery - Chris Hemsworth on Thor 2 set: