Comets hit the sun all the time. Far larger than the average meteor.
You might find this video, which looks as if the sun responds with a coronal mass ejection as a result of being hit by the comet.
But the comet is far too tiny to do this. It is just a coincidence. If you look closely you can also see that the coronal mass ejection happens before the comet could have hit the sun (sun shown as the white circle - the darker circle is an area that is blocked to protect the telescope).
Soho spots numerous comets and most of them dissapear before they hit the sun.
I don't know the answer to the question except to say pretty big.
I wouldn't be surprised if even an object the size of Mercury just melted into the sun with no effect. Except - if it had ice - a spectacular tail developing as it approached the sun before it hit it. But don't have any figures for that.