A conservative senator and early backer of Mr Trump, Mr Sessions has been dogged by allegations of racism which overshadowed his confirmation hearings.
The vote comes a day after the president dismissed Acting Attorney General Sally Yates, who questioned the legality of his immigration directive.
It imposes a temporary travel ban on seven, mainly-Muslim countries.
If Mr Sessions' nomination is approved by the judiciary committee, the full Senate - where Republicans hold a 52-48 majority - is expected to vote on it by the end of the week.