Bedford had already tapped the ball forward when he was caught by the swinging arm of Melican in the second quarter of the Swans' 14-point win at the SCG.
The Giants player passed a concussion assessment but was sent from the field under the blood rule for a cut to his right cheek.
He was later substituted out at halftime with blurred vision due to the swelling around his eye.
Melican could spend more than two weeks on the sidelines if the incident is graded as high or severe impact.
Sydney coach Dean Cox insisted Melican, who had checked on Bedford following the incident, did not act with malice.
"I've only seen it briefly. I understand that it'll go through the AFL and the tribunal situation," Cox said.
"Obviously, I hope Toby's OK. On top of that as well, Lewis has probably got an immaculate record.
"The way he plays his footy isn't malicious. He's always been a ball player."
Cox's GWS counterpart Adam Kingsley was circumspect when asked about the incident.
"It was over the other side of the field, so I didn't really see it," Kingsley said.
"I haven't watched the replay, so it's probably not fair for me to make comment on that."
Fremantle forward Patrick Voss was suspended for three games earlier in the season after he caught Richmond's Nick Vlastuin across the face with a swinging right arm.
Vlastuin suffered a nasty cut on his nose, with the incident graded as severe impact, high contact, and careless conduct.
A looming suspension to Melican only adds to Sydney's injury woes.
The Swans have 11 players sidelined through injury, nine of which are AFL mainstays, including captain Callum Mills (foot), Tom Papley (heel) and Errol Gulden (ankle).
Cox says midfielder Taylor Adams (hamstring) is the only player likely to be in frame to return against Essendon, with Mills remaining a week-to-week assessment.
Meanwhile, Melbourne forward Jake Melksham could come under scrutiny after nudging star Eagles defender Jeremy McGovern into oncoming traffic during a marking contest in Melbourne's 32-point win on Saturday night.
McGovern cannoned into the back of Demons forward Harrison Petty, with the incident concussing both of them.
Melksham took the mark but the umpire paid a free kick against him for the push.
The AFL have clamped down on dangerous pushes into traffic this year after Tigers young gun Sam Lalor broke his jaw during the pre-season.
Richmond's Rhyan Mansell copped a three-match suspension earlier this season for a dangerous push on Liam O'Connell that resulted in the St Kilda defender being concussed.
Melbourne coach Simon Goodwin launched a passionate defence of Melksham, adamant the incident was purely a football act.
Eagles debutant Bo Allan also faces a nervous wait for his swinging arm to the head of Jack Viney as the Demons tagger took a mark.
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