Dorset Police launched an investigation after the allegation by the steward following chaotic scenes at the end of the sides' Premier League game at the Vitality Stadium.
City's Raheem Sterling scored the winner in stoppage time and was sent off for a second yellow card because of his celebrations as supporters spilled on to the pitch, forcing stewards and police to intervene.
"The goal was followed by excited celebrations where a number of Manchester City supporters encroached on to the pitch," Dorset Police said in a statement.
They said two male spectators from Manchester were arrested as a result and that officers were reviewing CCTV of the pitch encroachment to establish whether any other offences may have been committed.
Bournemouth said the initial statement alleging assault had been withdrawn.
"AFC Bournemouth are aware of an alleged incident which occurred following Manchester City’s second goal at Vitality Stadium on Saturday," they said in a statement on the club website.
"The club have been advised that due to a misunderstanding, an earlier statement alleging assault has been withdrawn and no assault took place.
"AFC Bournemouth recognises that stewards and police were carrying out their duties in preventing encroachment on to the pitch, with the safety of players and supporters in mind."
Aguero had denied any wrongdoing.
"This allegation is false and the TV pictures prove it," he said on Twitter.
City manager Pep Guardiola was angry at referee Mike Dean's decision to give a second card to Sterling, who will now miss the next Premier League game at home to Liverpool.
"I don't understand. Hopefully, they can call me and explain the reason why," he said.
"He ran to celebrate. If you can't celebrate with the fans maybe we should play without fans."
(Reporting by Steve Tongue, additional reporting by Neville Dalton, editing by Ed Osmond)
