The loss of his relative has made Mr Zahawi “determined” to roll out the coronavirus vaccinations “as quickly as possible”, he told Good Morning Britain.
His uncle had been eligible for a jab but contracted the virus before he was able to receive it and “didn’t make it”, said the minister.
Mr Zahawi said: “It’s painful, and it’s closer to home than you think, Piers, in terms of losing relatives and family.
“I lost my uncle last week to Covid, but you’re right, it is grim and horrible but our way out of this is the vaccination programme.
“It makes me angry, but it makes me determined to make sure we vaccinate the most vulnerable people in our country and protect them as quickly as possible and then protect the whole nation.”
He added: “That is our way out of this, that is ultimately what we will do and I promise you I will make sure that happens.”
Mr Zahawi also said he is confident the UK will continue to receive deliveries of the Pfizer/BioNTech vaccines, amid threats from the European Union to block vaccine exports due to supple issues.
Speaking on Sky News, he said the UK’s vaccination programme was still on track and aims to offer all adults a first dose of the vaccine by the autumn and 15 million of the most vulnerable a jab by 15 February.
“Pfizer have made sure that they have always delivered for us, they will continue to do so,” he said when asked if the EU could prevent jabs from leaving its borders.
“They have made a very important announcement on the equitable supply of the whole world, including the European Union, and I’m sure they will deliver for the European Union, the United Kingdom and for the rest of the world.
“We have got 367 million vaccines that we have ordered from seven different suppliers, so I’m confident we will meet our target and continue to vaccinate the whole of the adult population by the autumn.”
It comes after Pfizer said last week it was delaying shipments of the vaccine for the next few weeks as it carried out work in its Belgian processing plant to increase capacity, cutting its initial deliveries to the EU by up to 60 per cent.
The EU on Tuesday by threatening to impose export controls on Covid-19 vaccines, accusing Pfizer of “lack of clarity and insufficient explanations”.