Between 13 and 15 tonnes spilled into the sea from the Brent Bravo, 116 miles north east of Lerwick, in May 2013.
Senior management from Shell were at Aberdeen Sheriff Court where the company admitted the release of fuel.
Sheriff Kenneth Stewart fined the company Â£6,650, reduced from the maximum possible due to the early stage of the guilty plea.
A Shell UK spokeswoman said: "We regret that the release occurred - no spill is acceptable.
"We have since carried out a thorough investigation into the incident and have shared the lessons learned across the business."
Oil giant Shell has been fined thousands of pounds after a diesel leak on board a North Sea platform.