The pair were scheduled to explain the Gupta family naturalisation saga after Mkhize and director-general Mkuseli Apleni did not appear before the committee last week.
It has been reported that while Gigaba was a home affairs minister, he went against the advice of a senior official of the department to waiver naturalisation of some of the Gupta family members who did not qualify for the status.
He has since denied that what he did was wrong.
At the start of Tuesday's meeting, committee chairperson Lemias Mashile said Mkhize apologised that she would be out of the country as she headed a delegation on behalf of Department of International Relations and Cooperation.
"However, she indicated that there will be an acting minister that she will inform to actually act on her behalf."
"Then the acting minister appointed for home affairs is Faith Muthambi but the acting minister has apologised because of prior arrangements and she is not here," Mashile said.
He also said Gigaba's apology was submitted by his parliamentary liaison officer, saying he would be unable to attend due to prior commitments.
"I hope that is an instruction or communication from the Minister of Finance who last week was out of the country," Mashile said.
Apleni, who could not attend last week's meeting, was in attendance with a delegation of department officials.
However, opposition party expressed their dismay that the two ministers did not turn up for the meeting.