The measure, which would prevent the layoff of thousands of postal employees and the closing of scores of mail-processing centers, was approved 62-37, CNN reported. But the bill appears unlikely to pass the House, which is considering its own legislation.
Rep. Darrell Issa, R-Calif., called the Senate bill "wholly unacceptable" in a statement.
A moratorium on the closing of postal facilities expires May 15, although the Senate bill would extend that.
The Postal Service reported losing $5.1 billion in the fiscal year that ended Sept. 30. It has lost ever more revenue as more people are using the Internet for business communication as well as personal messages.
The Senate bill would cap the salaries of top postal officials to the amount made by a member of the Cabinet and would make some cuts to employee compensation. It would also allow the postal service to adopt some cost-cutting measures like delivering mail only to the curb in some suburban areas.
Republicans in the House object to an increase in the amount the service could borrow from the U.S. Treasury.