Voters in Denmark, a relatively rich country, have rejected the treaty.
But the 11,000 island voters have rejected the treaty in six referendums since 1983.
One week earlier, voters in neighboring Norway had rejected the treaty.
Last week, Russia also indicated that it would reject the treaty.
Denmark, which rejected the treaty in a referendum June 2, said it would not try again until next year.
On March 19, 1920, however, the Senate rejected the treaty.
The other such country is Denmark, where voters narrowly rejected the treaty in a vote during the summer.
Congress rejected the treaty, and the issue smoldered for ten more years.
Egypt is lobbying other Arab nations to reject the treaty.
The Senate rejected the treaty by a vote of 61-38, less than the 66 required for ratification.