The government plans to raise fees above £9,000 for universities in England with "high quality" teaching.
But Exeter has announced that the increase will also be applied to current as well as new students.
The Liberal Democrats say they will table an amendment in Parliament to "stop this outrageous practice".
Exeter students have used social media to express their irritation at the increase.
Tim Quine, Exeter's deputy vice-chancellor, said: "The decision to charge £9,250 has not been taken lightly, but follows four years in which tuition fees have been frozen, while the costs of delivering a world leading education have continued to rise."
But Labour's education spokesman Gordon Marsden said Exeter's raising fees, before the increase had been approved by Parliament, was a "concerning and disturbing development".
Mr Marsden said students signed up for degree courses on the assumption that fees would not change - and that universities which introduced such increases would face "criticism for changing the goalposts in an unethical manner".
John Pugh, Liberal Democrat education spokesman, said the increase for current students was "completely unacceptable".
On the last day before the parliamentary summer break, the government published details of plans to allow universities to increase fees to £9,250 from 2017-18, scrapping the maximum upper limit introduced during the controversial trebling of tuition fees in 2012.
The plan would allow universities assessed as having "high teaching standards" to increase fees in line with inflation, calculated as 2.8% for next year.
Universities had begun to advertise these higher fees for students about to apply this autumn, for next year's courses.
But Exeter is also applying the increase to students already at the university.
The measure is permitted under the government's proposals, but many other universities have so far not made a decision on whether to charge higher fees for students who entered when the legal maximum was set at £9,000 per year.
The University of Nottingham has promised current students, and those about to start this autumn, that there will be no increase above £9,000 for the duration of their courses.
Exeter's website says that the increase for new and current students is "subject to approval from the government that we meet the criteria in the Teaching Excellence Framework".
The Teaching Excellence Framework is the system being created to measure the quality of teaching in universities.
For the first year, no universities have failed to reach the necessary quality threshold.
There was controversy over whether the university fee increase had been properly debated in Parliament.
Opposition MPs were angry that the higher fees were being announced before the Higher Education Research Bill, currently before Parliament, had been approved.
The government said the cap on fees could be lifted legitimately, via a statutory instrument, and that a vote would still be required if there was a challenge from MPs.
Both Labour and the Liberal Democrats have warned the government that they intend to block the planned increases and there were warnings that ministers had tried to "sneak out" the fee changes.
Universities had been accused by MPs of "disgraceful arrogance" in advertising higher fees before Parliament had approved them.
Universities have argued that a fixed upper limit of £9,000 has meant that the value of fees is being steadily eroded by inflation.
They have also voiced concern about the legal requirement to provide consumer information about forthcoming higher fees, to students applying this autumn, though a legal maximum of £9,000 remains in place until the proposed increase is approved.
Exeter University has told its current students that their tuition fees are going to be increased to £9,250 from autumn 2017.