The 25-year-old suffered the injury while he was keeping wicket for Somerset at the County Ground on Sunday afternoon.
"Obviously this is very disappointing for us at this stage of the campaign and it is also very disappointing for Craig," Somerset's director of cricket Dave Nosworthy told the county's official website.
"This was a freak accident and with him in such good form and in a good frame of mind with the bat and gloves, it has come at a bad time.
"However, he goes about things in a very professional way and with a good rehabilitation programme already planned we will have him back as soon as possible."
Provided that there are no setbacks in his recovery, Kieswetter should still be available for England at the Champions Trophy in June.