Police said they had also arrested a second "terrorist" believed to be an accomplice. The severely wounded soldier, a woman, was taken to hospital, the military said.
It was the latest in a series of stabbings targeting Israelis which, along with violent protests in the Palestinian territories, has raised fears of a full-blown uprising.
At least 47 Palestinians have been killed in an upsurge in violence since the start of the month, including alleged attackers. Eight Israelis have been killed in attacks.