Wednesday supporter Ben Ainsworth's vile views were aired in a series of tweets aimed at Sharp, whose son Luey passed away at just two days old in 2011 from a condition calledÂ gastroschisis.
Yesterday would have been Luey's seventh birthday.
Sharp had earlier netted a hat-trick as the Blades beat Wigan 4-2 to move back to the top of the Championship, prompting the tweets from AinsworthÂ '“Â the contents of which The Star will not repeat.
But they attracted widespread condemnation from fans of both city clubs. Owls fan '˜Me Me Froch' posted on Twitter: 'A poor excuse for a human being and as a Wednesday fan, I can say he is bringing our club into a very bad light.
'Apologies to Billy, SUFC and their fans for the childish behaviour'¦Â his family will be ashamed.'
Other fans called on Wednesday to ban the fan from Hillsborough. Blade Steve Food added on Twitter: 'Fortunately, he doesn't represent the views of anyone in our great city.
'Most football fans are intelligent and reasonable people; illiterates like that are the minority.'
A Twitter account, apparently opened by Ainsworth after losing access to his original one, later sent a tweet saying: 'Sorry to Billy Sharp and everyone who took offence to my tweets yesterday.'
A message from the account that originally tweeted the abuse later read: 'I'm sorry to Billy and his family, I don't know what I was thinking.
'Can't even remember doing it, I fully take responsibility and hope everything gets resolved.'
This episode is the latest example of Sharp and his wife Jade being attacked by trolls over the tragic death of Luey seven years ago.
In August, Jade bravely opened up to The Star in an emotional interview about Luey's death and how the period was 'a black hole'.
'I can never open that door, I can't ever go back there,' she added.Â I wonder if it'll come out when I'm older; if the gates will open a little. I had counselling, which was pretty raw, but still I couldn't get deep. My body has shut it down. It's gone."
Sharp poignantly played for Doncaster Rovers just days after Luey passed away. He scored a stunning goal against Middlesbrough and memorably unveiled a message under his shirt, reading: 'That's for you, son'.
Both United and Wednesday have been approached for comment. Â