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In a brief statement, Reid said there was no reason why concerns about the legislation cannot be resolved. He offered no new date for the vote, which had been scheduled for Tuesday.
Reid's action comes a day after a senior Democratic aide, speaking on the condition of anonymity, said the measure lacked the votes to clear a procedural hurdle and it was unclear if it could muster needed support.
The measure - known as the Protect Intellectual Property Act, or PIPA for short - is aimed at curbing access to overseas websites that traffic in pirated content and counterfeit products, such as movies and music.
Support for the Senate bill, and a similar one in the House known as SOPA, or Stop Online Piracy Act, has eroded in recent days because of fears that legitimate websites could end up in legal jeopardy.
Reid, in his statement, said, "In light of recent events, I have decided to postpone Tuesday's vote" on whether to begin consideration of the measure.
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Despite his decision to postpone action, Reid said, "There is no reason that the legitimate issues raised by many about this bill cannot be resolved.
"Counterfeiting and piracy cost the American economy billions of dollars and thousands of jobs each year, with the movie industry alone supporting over 2.2 million jobs," Reid said. "We must take action to stop these illegal practices."
Reid expressed hope that Senate Judiciary Committee Chairman Patrick Leahy, who has sought to help shepherd the bill through Congress, could help resolve differences in the legislation.
"I am optimistic that we can reach a compromise in the coming weeks," Reid said.
On Thursday, Senate Republican Leader Mitch McConnell urged Reid to postpone action on the bill.
Some senators who had co-sponsored the legislation dropped their support on Wednesday as protests blanketed the Internet, turning Wikipedia and other popular websites dark. Google , Facebook, Twitter and others protested the proposed legislation but did not shut down.
The entertainment industry wants legislation to protect its movies and music from counterfeiters but technology companies are concerned the laws would undermine Internet freedoms, be difficult to enforce and encourage frivolous lawsuits. (Reporting By Thomas Ferraro; Editing by Bill Trott)