Several others were shot in Pima County near Tucson today. At least four people are confirmed dead.
Witnesses told CBS Affiliate KOLD that the congresswoman was shot point-blank in the head.
Initial reports by KOLD that the Congresswoman was among the fatalities were corrected by her press people, who told KOLD that she is alive but in surgery.
"She is currently in surgery. She is still alive," said Darcy Slaten, Public Affairs, University Medical Center in Tucson.
Hospital spokespeople said Giffords is in critical condition. Eight other patients also at hospital are in critical or serious condition.
The assailant reportedly sprayed bullets into an area where the Democratic lawmaker was hosting a "Congress on Your Corner" event at a Safeway supermarket.
A law enforcement source told CBS News that a man apparently stood up in the crowd during the town hall meeting, shouted something and then opened fire. Someone - possibly police or security - then shot at the gunman.
The gunman has been apprehended but it is unknown if he was wounded.
A Federal law enforcement source tells CBS News that the suspect was born in 1988. No name yet being released. He is talking to authorities, but there is no evidence at this point that there is any other shooter involved.