The 27-year-old second-rower - who had been playing out of position at centre because of an injury crisis in the backs - was substituted towards the end of Rhinos’ Easter Monday defeat by Castleford Tigers and missed the win over Toulouse Olympique four days later.
“I’ve done a ligament in between my rib and my sternum,” Mellor revealed.
“It is causing a bleed internally, on my sternum.
“It has been quite scary really, but it is not too bad - it should be between four and six weeks.”
Mellor admitted he had “never heard of” this type of injury before.
“I did it in the Huddersfield game [almost two weeks ago], then tried jabbing it and playing with it against Castleford, but it was just so painful it was impossible to play,” he added.
“It is getting better now; any contact on it is like a shooting pain and when I sneeze and stuff it is painful, but apart from that it is getting better.”
Mellor is able to do some lower body work, including cycling, but upper body training is off the agenda for at least two weeks.
“It’s not ideal,” he conceded. “It’s just a case of trying to overcome it, which I will do.”
Mellor is one of several players in Leeds’ squad who has played under incoming boss Rohan Smith in the past and he believes the Aussie is the right man to revive Rhinos’ flagging fortunes.
“I loved working with him before,” he recalled.
“We had quite a good relationship and I think he will bring a new dynamic.
“He is quite youthful so he will bring a lot of energy and he has a lot of thoughts that are outside the box and ways that people might not have seen before, but if you commit to it I am sure it will work.”
Mellor believes Smith’s methods will suit the squad at Leeds.
“I think he will get the best out of the players we’ve got,” he added.
“We have obviously got some fantastic players with a lot of potential, which we’re not hitting at the moment.
“There’s a lot of players that will benefit from Rohan coming in.
“I think he will let us express ourselves and get the best out of each individual, which will result in a better team.”
Rhinos are Betfred Super League’s lowest scorers, having managed just 149 in the opening 10 rounds.
Mellor, though, believes Smith will put that right.
He said: “He is very attacking.
“I remember some of the tactics he brought in [at Bradford], he wanted us to kick-off short all the time and things like that.
“There’s a bit of excitement to it and I am sure he will bring loads more, he is a lot more experienced now.
“I think he’ll bring some exciting things and Leeds will be a more exciting team to watch, that score more tries and express themselves more.”
The prospect of working with Smith will make Mellor - who is out of contract this year - even keener to put his injury setback behind him.
“I am looking forward to playing under him again,” he said. “I seemed to understand him and he understood me, which is good. We will see where that leads.”