From the ATP World Tour website (emphasis mine):
Rafael Nadal captured an incredible 10th Monte-Carlo Rolex Masters crown on Sunday in beating fellow Spaniard Albert Ramos-Vinolas 6-1, 6-3 in the 76-minute final. Nadal’s 29th ATP World Tour Masters 1000 title, one shy of record-holder Novak Djokovic (30), marks the first time in the Open Era (since April 1968) that any man has won a singles tournament on 10 occasions.
From: Nadal Wins Historic 10th Monte-Carlo Title (Wayback Machine)
For WTA, there is a section Most titles / finals at a single tournament in the Wikipedia article WTA Tour records (current revision), which lists 12 titles of Martina Navratilova at Ameritech Cup (Chicago) as the record.
Information about most titles (and most consecutive titles) at a particular tournament is also given in the Wikipedia article Tennis tournament records and statistics (current revision). However, this article is not restricted to the Open Era.
EDIT: It is probably worth adding that no too long after this question Nadal won his 10th title in Barcelona. And in the same calendar year Nadal won his 10th singles title at French Open, becoming the first player to achieve this at a Grand Slam tournament.