McCarron picked up a hamstring injury in training, while McMahon is struggling with a quad injury which has been slow to respond to treatment.
Both are rated extremely doubtful for the first round tie, a repeat of last year's quarter-final, which Tyrone won.
Conor Meyler has recovered from a hamstring injury and is set to start.
McMahon's injury has kept him out of his last five club games and he is unlikely to feature as the Red Hands begin the defence of their provincial title against the Oak Leafers.
"Cathal McCarron has picked up a hamstring injury which is concerning, because it only happened about a week ago," said manager Mickey Harte.
"He has had a good couple of years for us and has a lot of ability in that sector of the field.
"Justin has picked up a lot of niggly injuries throughout his career. He has quad injury at the minute and has had it for four or five weeks.
"He's so versatile and so capable, and it's unfortunate, but we still have a lot of good players in the squad, a lot of versatile players."

Londonderry's Oxford Bulls was formed in October 2015 but have struggled to find another team to play against.
A plea was put out on social media several weeks ago to try to find them some competitors.
The team's manager then received a message from West Brom star McClean, which he thought was a "wind-up".
"Out of the blue I get a message from the man himself, James McClean, on Facebook," Kevin Morrison said.
"To be honest I thought it was one of those fake accounts, that somebody was taking the hand out of me.
"He said: 'I'm playing a match on Tuesday night, I'll be back in Derry at lunchtime on Wednesday - how does that sound?'"
Football strips and runners at the ready, it was still a surprise for Kevin Morrison's son when one of his idols joined them at the city's indoor football centre - and brought a few mates to make up a team.
West Brom forward McClean had featured in the Republic's friendly defeat by Iceland just 24 hours earlier.
"My wee boy, Adam, would be a big fan of his. James walked in and Adam was standing at the edge of the pitch," Mr Morrison said.
"He pointed at him, then he pointed again and then the jaw opened. He's was kind of star-struck for the rest of the game.
"I think it was a fantastic day, we're going to have some great memories to take away from it."
All the young footballers have a passion for the sport and the team has been set up with the help of the Foyle Down's Syndrome Trust.
It provides a wide range of activities for young people and adults with the condition.
Despite McClean's big match experience, Mr Morrison told the BBC that his young side gave the forward a good run for his money.
"He [McLean] had a fantastic attitude and they loved him for it," he said.
"The lads had a ball and James was an absolute gentleman, we couldn't believe our luck."
The team had initially tried to find a squad with similar abilities, but with no success.
After this week, the Bulls are now being offered potential tournaments against the likes of Manchester City, Everton and Liverpool.
"You have no idea the offers we've had, it's been crazy," Mr Morrison said.
"My phone is nearly melting. I've had hundreds of messages from mainstream football clubs right across the island, right over to England.
"[Northern Ireland winger] Paddy McCourt came down to help in training on Sunday as well, so it has been an amazing week and the boys have really responded to it.
"They've taken to it like ducks to water and I think we could have serious footballers on our hands before long," he added.
Tyrone look set to be without key defenders Cathal McCarron and Justin McMahon for their Ulster SFC opener against Derry at Celtic Park on 28 May.
[NEXT_CONCEPT]
Republic of Ireland footballer James McClean has surprised a team of children with Down's syndrome following a social media appeal.