The poster, which cropped up around south-east London, shows an upset child with his parents arguing in the background and the caption: "Dads - have the strength to change."
Campaigners for the UK-based group New Fathers 4 Justice have said they find the poster design "utterly offensive to men" and are calling for them to be removed.
They have also threatened to hold a "guerilla-style" protest against the council.
A US-based organisation Fathers4Justice has also labelled the posters a "hate crime" that "attacks" dads.
DADS Attacked with #HateCrimeAugust 17, 2015
Speaking to HuffPost UK Lifestyle, Al Ferguson from The Dad Network says that fathers should be "outraged" by the message given.
"When will the world realise that parenting equality is as important as equality in every other sense?" he asks.
"This is a clear ignorant oversight made by the campaigners to target dads. Domestic violence isn't gender specific so targeting dads is wrong.
"Dads should be outraged with this. It would have been very simple to create a campaign raising awareness of domestic violence without persecuting dads in the process," he adds.
Founder of Dads Matter UK, Mark Williams, says that it's important to not just single out fathers in these campaigns.
"In my experience of working with fathers, many have suffered in silence - even myself when I was with an ex-girlfriend.
"If we are going to stump out domestic violence it must be made aware that both mother and father can be targeted."
The controversial poster design is one of many issued by Greenwich Council over the past year.
One poster shows a man hiding his face, with the caption: "Don't turn a blind eye". The other poster features a little girl with a hand-drawn picture of a sad face placed in front of her head. The caption reads: "You can't hide domestic violence from children."
In response to the backlash, a spokesperson for the Royal Borough of Greenwich council said: "The Council agrees that Domestic Violence is utterly unacceptable regardless of who is causing it. We also recognise that the overwhelming majority of men are good fathers and role models to their children and this campaign is not meant to detract from that.
"This is our third set of posters designed to help victims - both men and women - to come forward and seek help and they also show the impact it can have on young children.
"This single poster was developed as a result of evidence which shows that fathers who are abusive to their partners are more likely seek help to change their behaviour if they are made to face up to the damaging effects their behaviour has on their children. Whilst women can also be the cause of domestic violence, the majority of incidents are committed by men.
"The Council is committed to tackling the cause of the issue with our partners and has funded a dedicated police Domestic Violence Intervention Team to ensure victims of domestic violence do not feel helpless or suffer in silence.
"We therefore welcome the debate about our campaign so that these important issues can be brought out in to the open and discussed. It will help the Council to get across our message that local residents can do something if they are worried a friend, relative, neighbour or stranger may be suffering domestic violence or abuse behind closed doors."
[H/T Metro]Suggest a correction