Northern is implementing increases of up to 50p from 21 May to "bring fares in line with other areas".
The RMT union said the "latest fares rip off is just another example of costs being shifted" to passengers.
Northern, which has introduced rises since September 2016, said fares in the area have been "historically low".
The rail operator said there would be an increase "of no more than 50p" on the majority of off-peak day returns and singles for journeys made within Greater Manchester.
It said there would be no change to anytime day single, anytime day return or weekly season tickets and Transport for Greater Manchester concessions.
There would be reductions on some tickets, it added.
Northern said the rises were to make fares "fair and consistent" across the network.
RMT general secretary Mick Cash said: "This latest fares rip off is just another example of industry costs being shifted to the passenger."
Rochdale councillor Andy Kelly said the hike was "the great rail rip off " and would "affect the poorest".
"Many commuters tell me that they have changed their shift patterns to take advantage of off-peak discounts."
Northern said the travel increases would go towards its modernisation programme which will see it get rid of Pacer trains by 2020.
Rail workers on Northern, Southern and Merseyrail have gone on a number of strikes with the latest on 8 April over proposals for driver-only-operated trains.

The conservationists have described it as a major milestone, there are thought to be about 70,000 coins in the hoard.
By the end of the day on Friday the team had removed 55,014 coins, 63 more than the previous largest Roman Cunetio hoard found in Wiltshire.
The team are clearing the coins in view of the public in a special laboratory at La Hougue Bie Museum in Grouville.
The Jersey Heritage team has spent two years removing the coins one by one from the hoard discovered by two metal detector enthusiasts in 2012.
The value of the hoard will not be known until next year when the States will have to decide whether to pay to keep it in the island.

Martial has been linked with a move to Inter Milan as part of a deal that would see Ivan Perisic leave the Italian club.
The 21-year-old created Jesse Lingard's first-half opener in the 1-1 friendly draw with Real Madrid in Santa Clara.
"He is a young player. He still has time to learn, to improve and develop," said Mourinho.
"We want more consistency in his talent."
United have not managed to get the best out of 21-year-old Martial since his £36m move from Monaco in 2015.
He set up Lingard's goal in California on Sunday with a fabulous piece of skill that took him past Luka Modric and Daniel Carvajal.
United won the game 2-1 on penalties.
"I can say he is training better than before and is working harder than before," added Mourinho.
United, who are unbeaten in four pre-season games, have one match remaining in the United States, against Barcelona on Wednesday.
They flew out of California straight after the game to Washington DC, where they will spend the next three days before the trip home.
It is a major difference to 12 months ago, when Mourinho and his squad went to China and had a planned match against Manchester City in Beijing cancelled due to the poor state of the pitch at the Bird's Nest Stadium.
Mourinho said: "We were based in Los Angeles for 15 days, which was fantastic. We were always in the same hotel and on the same training ground.
"Now we go to DC which is halfway home almost. These next three days are a good thing for us on our way back.
"If Juan Mata (ankle) and Ander Herrera (hip) are not a real problem in terms of injuries, I would say it has been a perfect pre-season for us."
Prior to the game, Mourinho said it would be "mission impossible" to try and sign Gareth Bale from Real Madrid, so he had not even tried.
Speaking after the match, whilst perfectly polite, it was clear Bale was not interested in talking about his future in Madrid.
Question: Jose Mourinho says it would be mission impossible to get you to Manchester United.
Answer: There you go.
Question: Is that the way you see it?
Answer: I haven't said anything.
Question: You continue to be happy at Real Madrid?
Answer: Yes.
Rail fares for some off-peak Northern services in Greater Manchester will be increased by up to 10% - the third rise within the past year.
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The team removing coins from the Jersey Celtic hoard have gathered more than in any other British hoard to date.
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Manchester United manager Jose Mourinho has told forward Anthony Martial he needs to be more consistent.