A police patrol was sent to Oldham after the EDL fuelled false rumours of 'Muslim celebrations' over the Woolwich attack in London.
Greater Manchester Police said the episode should remind people to consider what they put on social media when tensions are running high.
A Twitter-user had claimed police were 'trying to disperse hundreds of Muslims' in the centre of Oldham who were celebrating the murder of the soldier.
The English Defence League then passed the rumour to its 19,000 followers, and word quickly spread on the social networking site.
It took a visit from Greater Manchester Police to confirm there was no basis to the claim.
The man who had claimed to have witnessed the clash later backtracked, claiming he "was only driving through" and had not managed to photograph the scene.
A Greater Manchester Police spokesman said the rumours had been fuelled by the EDL tweet.
He said: "We had not had any protests, but sent a patrol there just in case.
"With things as they are, you have to be very careful what you are putting on social media."
He said no action would be taken against those who had spread the false rumours.
The victim of the attack has since been named as Drummer Lee Rigsby.
Suggested For You
Get top stories and blog posts emailed to me each day. Newsletters may offer personalized content or advertisements. Learn more