Ehiogu's inclusion provoked anger on social media.
Tom Wainwright said it was "sick" that punters could bet on the former centre-back, while David Kelly said it was "pretty poor taste".
Matt Zarb-Cousin, from the Campaign for Fairer Gambling and a former spokesman for Jeremy Corbyn, said he hoped it was "a mistake not a joke".
Replying to Twitter users individually, Paddy Power said it was "a genuine error, which was removed as soon as we realised. Apologies".
The company later issued a statement to the Press Association, adding: "This was a genuine error, a trader re-used an old market as a template for this one, and didn't notice that Mr Ehiogu was included.
"Obviously, that was a mistake, one which was rectified as soon as it was spotted, within minutes."
A spokesman said customers were able to put money on Ehiogu for "less than five minutes" before the error was discovered, adding that nobody actually placed that particular bet.
He added: "We would like to apologise to Mr Ehiogu's family if they did see the tweet.
"It was obviously a mistake and no offence was meant."