Cleveland.com reported earlier that police in Cleveland were investigating a sexual assault allegation against Salazar. According to Bastian, the city prosecutor's office was presented the case on Wednesday before deciding not to file charges.
The incident that was being investigated reportedly occurred early in the morning on Jan. 23.
The Indians previously released a statement saying they were aware of the allegations and had no additional comment at the time.
Salazar, 25, started 20 games for the Indians in 2014 and made 11 starts at Triple A. He had a 4.25 ERA with 120 strikeouts and 35 walks in 110 major-league innings last season.
Cleveland's pitchers and catchers report to spring training in Arizona on Feb. 18.
- Dan Gartland