The fire, at the new Kings Place development in York Way, caused the closure of the King's Cross main line station.
A London Fire Brigade spokesman confirmed that half of the eighth floor was engulfed with flames and that one person had been taken to hospital with burns.
Four fire engines attended the site where fears of gas canister explosions caused a 200-metre cordon be thrown around the site of the blaze.
Guardian Newspapers will occupy half of the building which will become its new London headquarters. The newspaper group is set to bring together its 1,400 strong staff - which are currently scattered across seven sites in the Farringdon area - to one building.
The development will combine an office building with restaurants, music and arts facilities and is due for completion in 2008.
Main contractor Sir Robert McAlpine was appointed by developer Parabola Land in June 2005. Dixon Jones is the architect on the project.
York Way is closed both ways between Pentonville Road and Copenhagen Street.