The soap actors had tweeted about the singer's rumoured relationship with former boyfriend Chris Brown, who was charged with assault against her in 2009.
Dawson - who plays Darren Osborne in Hollyoaks - tweeted: "I hear Rihanna is back with Chris Brown... well if you can't beat 'em, join 'em!!"
Later, Coronation Street star Thomas (Jason Grimshaw) retweeted the message.
With the ITV and Channel 4 soaps both featuring domestic violence plots in recent months and supporting related charities, campaigners have since condemned the pair's comments.
Women's Aid member Teresa Parker told The Sun: "Jokes like this one trivialise a very serious issue.
"We have worked with Hollyoaks and Coronation Street to help develop domestic violence storylines and we hope they explain to the actors involved why domestic violence just isn't funny."
A TV source added: "Both lads are going to be in trouble. It's madness to post comments about one of the most highly publicised cases of domestic violence when your wage comes from shows filled with domestic violence plotlines."
Following the complaints, a Hollyoaks spokeswoman said: "This is not the sort of comment we would ever sanction. We will be talking to the actor."
An ITV spokeswoman added: "We will look into the situation on Monday."
Rihanna and Chris Brown have been rumoured to have reconciled in recent weeks, with the pair reportedly planning to go public after she releases her new album Unapologetic on November 19.