He admitted that the target was “stretching” but voiced “confidence” that it would be achieved.
Military logistics chiefs are involved in the NHS roll-out of the vaccine.
Dozens of hospitals are already delivering vaccinations, with GP hubs, huge vaccination centres, as well as pharmacies part of the huge vaccination programme.
Mr Zahawi insisted that more than two million jabs a week could be delivered to reach the target of more than 13 million people most at risk from Covid by mid-February.
He told Sky News: “It’s a big target, and I think the Prime Minister is right to set challenging targets.
“We need to get on with this and do it as quickly but as safely as possible, which is why I commend the NHS for the plan that they put in place.
“The military are embedded in the team.
“So it is a coming together of the nation to deliver this.
“It is a stretching target, no doubt… very stretching target.
“But I’m confident that with this plan that the NHS have put together we will deliver this.”
Daily figures will be published from Monday on how many people have been vaccinated.