The NSA was allowed to collect this information without a warrant thanks to a US law passed in 2008.
In a statement it said that an internal review had revealed several problems with the spying programme and its effect on US citizens' privacy.
Surveillance experts said the NSA's decision was "very significant".
The NSA is not allowed to conduct surveillance within the US but it managed to skirt this restriction thanks to one section of the 2008 Foreign Intelligence Surveillance Act (Fisa).
This let it grab the phone calls and messages of US citizens which mentioned or otherwise involved people outside the US it was keeping an eye on.
The NSA had been widely criticised because using Fisa had meant it had scooped up lots of messages, texts and other material sent by Americans without having to apply for a warrant.
In its statement, the NSA said technical limits, privacy problems and the difficulty of carrying out this type of surveillance had driven its decision. It also said it would delete the "vast majority" of data collected via this spying programme.
The powers to spy outlined in Fisa were due to be scrutinised this year by the US Congress and are set to be renewed by the end of 2017. Many members of Congress have been critical of the spying effort and politicians were expected to significantly limit its scope during the renewal and review process.
The Fisa spying programme has also been criticised by the US Federal Intelligence Surveillance Court, which oversees NSA requests for surveillance warrants.
The NSA had defended the Fisa-allowed spying, saying that it had helped it gather "critical" intelligence.
Julian Sanchez, a privacy and surveillance expert with the Cato Institute, said the broad reach of Fisa-sanctioned spying had made it a key target of civil liberties campaigners.
"Usually you identify a specific individual to scrutinise their content; this was scrutinizing everyone's content to find mentions of an individual," Mr Sanchez told Reuters.
The US National Security Agency (NSA) is to end surveillance on messages sent by US citizens that mention foreign intelligence targets.