The previous day had seen home favourite Michaella Krajicek accept the proposal of men's player Martin Emmrich on court after safely negotiating her first-round match, but there was to be no happy ending for Cibulkova at the WTA International grass-court event.
The Slovakian slipped to a 2-6 6-3 3-6 defeat at the hands of Kazakhstan's Yaroslava Shvedova, falling at the first hurdle to a player ranked 57 places lower.
After dropping two service games in the opening set, Cibulkova bounced back to outnumber her opponent by two breaks to one in the second.
However, Shvedova reversed that achievement in the third to set up a second-round clash with the newly engaged Krajicek.
Third seed Eugenie Bouchard also fell victim to an upset in a 6-2 3-6 3-6 defeat to world number 75 Vania King.
Bouchard opened up a 4-0 advantage on her way to winning the first set, but King's serve remained unbroken for the remainder of the clash as he ensured her progression.
Elsewhere in the first round, French Open runner-up Simona Halep cruised through with a 7-5 6-2 victory against qualifier Olga Govortsova, and Carla Suarez-Navarro enjoyed a relatively comfortable 6-4 6-2 triumph over Barbora Zahlavova-Strycova.
Andrea Petkovic was the highest-profile casualty in the day's second-round matches, losing 4-6 7-6 (7-4) 5-7 to Magdalena Rybarikova, while Garbine Muguruza was a 6-4 6-1 winner over Yvonne Meusburger.