The MP for Aberavon posted a picture of the pair on Twitter on Sunday. They sat two metres apart and had set up chairs outside the senior Mr Kinnock’s house. But South Wales Police were quick to respond to remind then self-isolation rules apply to everyone.
But the MP responded he felt the visit was essential due to him dropping off food and supplies.
He responded on Twitter: "I felt that this was essential travel as I had to deliver some necessary supplies to my parents.
"I stayed long enough to sing 'happy birthday' to Dad, and I was off.
"All the best, Stephen."
His father has been self-isolating due to being over 70 amid the coronavirus pandemic.
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Helle Thorning-Schmidt, former Danish Prime Minster and wife to the MP, also posted about their visit to Mr Kinnock on his birthday.
She wrote in a series of posts on Twitter: “Socially distanced visit to my in-laws.
"Normally we would have a big family lunch. Happy birthday dear Neil.
Rachel Kinnock also made a visit to her father.
She wrote on Twitter: “We were able to safely deliver a cake, a crumble and a lamb curry!”
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As of Sunday, 19,522 people in the UK have tested positive for coronavirus.
According to the government's website, 1,228 patients who have contracted the lethal virus died.
Prime Minister Boris Johnson has warned that tougher lockdown measure may come.
He said: “We will not hesitate to go further if that is what the scientific and medical advice tells us we must do."
The MP posted: “Dad turned 78 today. Incredible, but true.
“Helle Thorning and I took a couple of chairs over, and sat in their front garden for a socially distanced celebration. As you do."
Mr Kinnock signed off his tweet with ,“Happy birthday, mate. “
South Wales Police responded: ”We know celebrating your Dad's birthday is a lovely thing to do, however this is not essential travel.
"We all have our part to play in this, we urge you to comply with government restrictions, they are in place to keep us all safe.”