“Where is Boris?” Mr Hunt asked the room during the debate.
“If Boris team won’t let him out to debate five pretty friendly colleagues, how will he get on with 27 EU countries?”
The foreign secretary had been asked how he could seriously contemplate a no-deal Brexit.
“[Boris] should be here to answer that question,” he said, before discussing his views on no-deal.
Mr Johnson is widely considered the front runner in the race to replace Theresa May but was the only candidate who refused to participate in Sunday’s debate.
The former foreign secretary is also yet to confirm his participation in hustings with political journalists on Monday.
Channel 4 has placed an empty podium in the debate room to mark Mr Johnson’s absence.
Before the debate began Rory Stewart said he was “looking forward” to the debate and hoped that Mr Johnson was going to ”make a last-minute appearance”.