The pair of ailments were sustained late into the Bombers' 22-point loss, compounding the club's woes as Essendon enter next week's clash against reigning premiers Melbourne without a win to their name this season.
Cox could be in doubt for the Round 3 encounter, while the diagnosis for Merrett is looming to be a major blow for Ben Rutten's planning.
Merrett has seemingly sustained a syndesmosis injury, a setback that could rule the star Bomber out for multiple months after requiring surgery.
“Zach and Nik had scans this morning and have both suffered ankle injuries, with Zach expected to have a longer stint on the sidelines,” Essendon GM of football Josh Mahoney said.
“We will look at surgery as an option for Zach but it is likely he will miss around six to eight weeks.
“Nik’s injury isn’t as severe so we will assess his recovery this week and give him the best chance to get up for our match against Melbourne.”
Speaking post-match on Saturday, Rutten spoke on the suspected extent of injuries to his young utility and star midfielder.
"Coxy's had a reasonably solid rolled ankle. Just a standard rolled ankle at this stage," Rutten said.
"Zach's an ankle as well but I think more at the minor end of it at this stage but that's the information I've got at the moment."
Last week's dazzling debutant Nic Martin was also ruled out of Round 2 after being forced to follow the AFL's health and safety protocols, with the West Australian expected to return for next Friday's clash with the Demons at the MCG.
Midfielder Dylan Shiel was withdrawn from Rutten's selection planning for this weekend, with the former Giant required to prove his fitness in the week ahead.
"Not a long-term thing. He'll have to get through training," Rutten added.
"We'll get Nic Martin back from COVID protocols, Shiel hopefully available."
Will Snelling (calf), Harrison Jones (ankle), Anthony McDonald-Tipungwuti (personal), Zach Reid (foot) and Michael Hurley (hip) also add to Essendon's extensive injury list early into their 2022 campaign.
Rutten's side are facing the likelihood of starting the season 0-3 as they enter next week's match with Melbourne unfavoured. The Bombers will face Adelaide, Fremantle and Collingwood in the succeeding rounds.