Arrington, 47, was the passenger in a car driven by a friend on Friday night when a vehicle traveling in the wrong direction struck them on Highway 17 in Charleston County as they were going to Hilton Head where Arrington was to receive an award from a state medical organization, her campaign said.
Campaign spokesman Michael Mule said Arrington will definitely stay in the race for Congress.
"She's determined, if not more than ever, to get back on the trail," Mule told the Post and Courier newspaper of Charleston.
Tim Scott, a Republican US Senator from South Carolina, told the same newspaper, "There is no doubt she will make a strong recovery."
Arrington broke her back and several ribs, and sustained injuries that required her to undergo major surgery including the removal of a portion of her small intestine and part of her colon, her campaign said in a statement.
It said a main artery in one of Arrington's legs collapsed and that she will require additional surgery and will be hospitalized for two weeks.
Local media said the candidate's friend, Jacqueline Goff, 59, of Mandeville, Louisiana, was in critical condition.
The Charleston County coroner's office named the woman killed in the crash as Helen White, 69, of Ravenel, South Carolina.
Arrington, a state representative, defeated Sanford, who at times was critical of US President Donald Trump in a primary on June 13.
She made Sanford's criticism of Trump a theme of her campaign, and the president weighed into the race, tweeting hours before the polls closed that Sanford was "nothing but trouble" and "very unhelpful to me."
Trump tweeted on Saturday that his "thoughts and prayers are with Representative Katie Arrington of South Carolina, including all of those involved in last nights car accident, and their families."
Sanford said on Twitter his thoughts and prayers also went to "Arrington, her family and those involved in last night's automobile accident."
Arrington's Democratic opponent in the fall election, Joe Cunningham, said in a statement he and his wife were praying for Arrington and that he was suspending "all campaign activities until further notice."