Dyer pleaded guilty to religiously aggravated harassment at Westminster Magistrates' Court on Friday.
He was fined £400 ($806). It would have been £200 but the court doubled the fine after an application by the Crown Prosecution Service who argued that the offence was motivated by and showed hostility towards members of a religion.
"Dean Dyer denied being a bigot but his actions have proven otherwise. Today, he has admitted his guilt and will now pay for price for his actions," said Emma Lineton of the West Midlands Crown Prosecution Service.
"Anti-Muslim abuse is a serious issue and has no place in society. We will not tolerate it in any way, shape or form."
His conviction comes on the same day that the CPS published its annual hate crime report, which showed that 605 cases were prosecuted as faith-based hate crimes in England and Wales in the 12 months to March this year. Of those, 507 ended in a conviction and 76 per cent of those received a sentence uplift to reflect the true nature of the hate crime.