"Our 150-year-old mastheads are on their knees after years of cost-cutting and private equity companies are circling."
The no-confidence motion further accused Mr Hywood of allowing quality journalism to "wither" when he should have been seeking "ingenious ways" to sustain it.
Some of the most senior writers in Australia were absent from covering Tuesday's federal budget due to the strike.
Many Fairfax employees took to Twitter on Wednesday to urge readers to subscribe and help secure the mastheads' future.
But in an internal email, staff were told they could be fired if their use of social media breached company policies.
The email warned against belittling colleagues who chose to work during the strike. Fairfax also said it wouldn't tolerate employees "encouraging members of the public, including subscribers, to boycott Fairfax Media products during industrial action".
More than 10,000 people have signed a petition to save Fairfax jobs.
Hywood last week told investors the company would push ahead with the cuts to get Fairfax on a sustainable footing.
The Media, Entertainment and Arts Alliance union said the strike had placed the future of journalism firmly in the spotlight and resulted in a Senate inquiry.
"Public-interest journalism is vital for a healthy democracy," MEAA chief executive Paul Murphy said.
The Senate committee will report by December and investigate factors including the role of government in ensuring a viable, independent and diverse media as well as "fake news" and its circulation on social media.
Greens Senator Scott Ludlam is concerned about the commercial imperatives "taking over" Fairfax, which he said was "effectively being asset-stripped".
"That's a disaster not just for Fairfax but for the rest of the country," he told reporters in Canberra on Wednesday.
The strike also drummed up support in the NSW upper house, which has passed a motion declaring "a properly funded media supports the operation of government and democracy in NSW".
Fairfax declined to comment when contacted by AAP.