The woman, who is a British national and had been working aboard the installation, was detained by the offshore installation manager.
The alert, at 0920 GMT, resulted in 539 people being taken off the Flotel Safe Scandinavia platform.
However, all personnel are now being allowed back on.
Grampian Police said it did not consider that the incident had been terrorist related.
The accommodation platform is 130 miles off the Aberdeen coast.
Scotland's Justice Secretary Kenny MacAskill was being kept informed about the operation.
A Scottish Government spokeswoman said: "A Scottish Government civil contingencies official is based in the Grampian Police control room, and the justice secretary is being regularly kept appraised of developments.
"There are well established procedures for dealing with incidents in the North Sea, and these are operating efficiently and effectively."
Source: BBC News