Just one month after the start of a review of all the city's bus lanes, the council has decided to suspend the camera in Great Western Road at Shelley Road near the Beatson.
The launch of the seven-month review followed a storm of complaints from motorists who felt they had been unfairly hit with penalties.
The camera will be suspended until the result of the review is known.
But insiders say it is unlikely to operate in its present location in future.
The Beatson bus lane camera was installed in December, last year, and is in operation from 7am until 9.30am and between 4pm and 6.30pm from Monday to Saturday.
Despite only being in operation for five hours a day, in January it caught 1339 drivers.
Council leader Gordon Matheson said: "The council is currently undertaking a review of the location and operation of all bus lanes in the city.
"I am aware of the particular concerns raised regarding the camera in Great Western Road at Shelley Road.
"Given the particular sensitivities of this camera in relation to the Beatson, I have asked officers that no infringements of this bus lane are processed during the review.
"I am sure this will provide reassurance to the patients and their families accessing the Beatson by car."
Roads bosses insist bus lanes are "vitally important" in keeping the city moving, improving traffic flow on congested roads and increasing the reliability of public transport.
Earlier this year the Evening Times highlighted the fact that the council fined motorists for driving in bus lanes on Christmas and New Year's Day - despite there being no buses on the roads.
They include a man sent a fixed penalty notice for driving in a bus lane as he rushed to his dying mother-in-law's bedside on December 25.
Following a flood of complaints, the council decided to introduce a pilot scheme which will operate only on the two quietest days of the festive season.
That will result in bus lane cameras remaining on, but drivers who use them on December 25 and January 1, when buses are off the road, will not face fines.
In August last year, the council revealed the number of motorists illegally driving in city bus lanes had more than halved in the past year.
In May 2012, a total of 18,035 fixed penalty notices were issued but in May last year, the figure had fallen to 7645 - a drop of 58%.