Campaign spokesman Mike Ras says the texts were sent to a couple of campaign workers over the last few weeks.
He says police were called in and investigators have indicated that an arrest has been made.
Ras says he can't comment further because the police investigation is ongoing.
Toronto police aren't confirming charges, but radio station Newstalk 1010 is reporting that the suspect has already appeared in court and was released on bail.
Elliott is one of the leadership hopefuls vying to replace Tim Hudak who resigned last year.