Watson, a member of the Commons culture, media and sport select committee, suggested that it was "only a matter of time" before the News International title became embroiled in the scandal.
"Do you really think hacking only happened on the News of the World?" he asked the Labour Party conference today.
Watson used a debate on phone hacking to suggest that the practice may not have been confined to the News of the World, the News International paper that was closed down in July.
He said: "Do you really think hacking only happened on the News of the World? Ask Dominic Mohan. He is the current editor of The Sun.
"There should also have been an element of shame because for years [politicians] were complicit in propping up Murdoch's power."
Watson added: "Ask the editor of The Sun if he thinks Rupert Murdoch's contagion has spread to other newspapers.
"Ask him, and if he gives you an honest answer, he will tell you that it is only a matter of time before we find The Sun in the evidence file of the convicted private investigator that hacked Milly Dowler's phone."
Mohan became editor of The Sun in 2009, after previously being deputy editor and features editor. He also briefly worked at the News of the World in the mid-1990s.
Watson also attacked News International chairman James Murdoch, who has been recalled to clarify statements he made on phone hacking to the culture committee.
Murdoch has claimed that he was not aware of evidence indicating that hacking was more widespread at News International, despite contradicting statements from staff at the firm.
Watson feels that Murdoch was "certainly not a fit and proper person" to be chairman of pay-TV giant Sky, and also questioned whether the Murdoch-controlled News Corporation should continue to own a 39.1% stake in the broadcaster.
"[News Corp] is a company sick with corruption and criminality from top to bottom," he said.
"That much has been proved. The Murdochs and their minions have consistently and blatantly lied to our courts and our parliament."
There have been 16 people arrested to date as part of the police investigation into alleged hacking at the News of the World.
Parent firm News International, which is also conducting an internal inquiry into practices at the group, declined to comment on Watson's remarks.
Also today, shadow culture secretary Ivan Lewis told News Corp boss Rupert Murdoch that "never again" will he be able to assert political influence over UK politics in "the pursuit of your commercial interests or ideological beliefs".