Rune trailed 2-5, 40/15 on the Van de Zandschulp serve in the third set as he battled a problem with his upper right arm.
Van de Zandschulp led 4-3 in the first set, and Rune was serving at 40/15 when he quit due to a sore chest.
The Norwegian's defeat came at the hands of Dutch player and eighth seed Botic van de Zandschulp.
The match of the day was undoubtedly played between Alex Molcan and Norbert Gombos with the scoreline reading 6-1, 3-6, 7-6 (9-7).
The BMW Open has always had a reputation of being action-packed and looking at the entries, this season will be no exception.
Meanwhile, Hugo Nys and Tim Puetz bag their maiden ATP Tour team title at the Millennium Estoril Open.
Elsewhere, Cameron Norrie downs Marin Cilic in a tight contest to enter Estoril final.
The Belarusian came from a set down to defeat the German favourite in a three-set thriller to set up a semifinal clash against Jan-Lennard Struff.