Greater Manchester Police said the 37-year-old surrendered to Cheadle Heath Police Station on Wednesday morning.
Officials said they couldn’t confirm the man’s identity at this point, but said he was from Ashton-Upon-Mersey.
He was arrested on suspicion of violating the Malicious Communications Act and remains in detention for questioning.
It comes after Andrew Bone, a 37-year-old commercial building manager from Greater Manchester, was suspended by his employer Savills for a racist tweet about England footballers.
He reportedly contacted police claiming his Twitter account was hacked when the message was posted on Sunday night.
Detective Inspector Matt Gregory said: “The actions of a small number of people overshadowed what was an extremely unifying event for our country on Sunday night. We are firm in our commitment, any racist abuse whether online or offline is not acceptable.
“We now have a man in custody and our investigation is continuing. “
It comes after two men were arrested by West Mercia Police amid racist abuse targeting Marcus Rashford, Jadon Sancho and Bukayo Saka following England’s loss to Italy on penalties.
A 50-year-old man from Powick, near Worcester, has been arrested on suspicion of inciting racial hatred.
Media said the tweet said Rashford’s MBE “needed to burn your scythe” and added that he should return to his “own country”.
The force also arrested and released a man in his 60s from Shropshire after racist comments were posted on Facebook.
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The man, believed to be a town councilor who later resigned from Pontesbury Parish Council, said his Facebook account was hacked.
The inquiries come after unrest at Wembley on Sunday, as fans without tickets forced their way into the stadium.
Police are also investigating “random attacks on Italians” launched by English supporters after the final.
Cheshire Police Chief Mark Roberts, who is the national football police official, said The independent: “We have seen random attacks against Italians… Italians celebrating victory have been attacked.
“We haven’t seen massive numbers, but there have been way too many. We see these incidents when England is eliminated from tournaments in terms of targeting foreign nationals. “
Forces across the country are still pulling together numbers on the number of incidents targeting Italian fans, who won the tournament on penalties.
More than 2,300 Euro-related police incidents have been recorded so far, surpassing the 2018 World Cup to make it the worst football tournament ever recorded for crime.
They include stabbing, stabbing, fights and assaults on police officers, with at least 622 people arrested to date in England and Wales.
Anyone with information about abuse of England players is asked to contact Greater Manchester Police on 0161 856 4973 or call Crimestoppers anonymously on 0800 555 111.