The final had been pushed back a day after rain forced Sunday's contest to be postponed. Sherif, 30, was firmly in control at 6-4, 4-0 when Badosa was unable to continue after 70 minutes of play.
The Egyptian seized the pivotal break in the seventh game of the opening set before taking complete command early in the second, breaking Badosa's serve in each of the first two games.
The triumph marked her first WTA Tour-level crown since winning the clay-court Parma Open in Italy in October 2022, with both of her tour titles coming on the surface.
At the Livesport Prague Open, top seed Marie Bouzkova delighted the home fans by overcoming Spain's Jessica Bouzas Maneiro 7-5, 7-5.
Fellow Czech Dominika Salkova also advanced, defeating sixth-seeded Croatian Antonia Ruzic 7-6 (2), 6-4 despite surrendering a 4-0 lead as Ruzic claimed the next five games. Salkova captured 52.2% of return points and finished with a 5-4 edge in service breaks.
Elsewhere, eighth seed Daria Snigur of Ukraine beat Germany's Ella Seidel 7-5, 3-6, 6-3, Turkey's Ayla Aksu rallied past Belgium's Sofia Costoulas 2-6, 6-3, 6-4, Czech Lucie Havlickova defeated Alycia Parks 6-2, 6-4, Carol Young Suh Lee overcame Ukraine's Veronika Podrez 6-1, 5-7, 6-2, and France's Oceane Dodin dispatched Czech Alisa Oktiabreva 6-3, 6-3.
In Hamburg, second seed Anhelina Kalinina opened her campaign with a 7-5, 6-4 victory over Spain's Kaitlin Quevedo, converting eight of 17 break-point chances despite recording no aces and nine double faults in a match featuring 14 return games and eight service holds.
Hungary's Anna Bondar beat Japan's Moyuka Uchijima 7-5, 6-4 after winning 48.4% of return points, while German wild card Julia Stusek produced the day's standout battle by defeating Argentina's Nadia Podoroska 4-6, 6-3, 6-4.