Swiatek, the world number three, fell to American Emma Navarro 7-5, 2-6, 6-3 just days out from Wimbledon, while Andreeva lost in straight sets to Russian compatriot Ekaterina Alexandrova in the key Wimbledon warm-up tournament.
Playing her first match since she was eliminated from the French Open, a tournament she has won four times, Swiatek struggled early, with Navarro winning the first three games.
Swiatek forced her way back, but a series of double faults, including on the final point of the set, allowed the American to claim the opener.
The 25-year-old found her feet to claim the second set, dropping just two games, but Navarro fought back and broke Swiatek to claim the third set and the match in two hours and five minutes.
"It was hot out there and I didn't have a ton of rhythm, I think both of us felt that throughout the match. So it came down to a lot of serving," Navarro said.
"I relied on my serve there at the end and it ended up getting me through."
In the quarter-finals, Navarro will face Romanian Elena-Gabriela Ruse, who beat Russian Anna Kalinskaya 7-5, 6-2.
Earlier on Wednesday, French Open champion Andreeva fell in her first match since her Roland Garros victory, losing 6-3, 6-4 to Alexandrova.
World number five Andreeva, playing her first match on grass in 2026, pulled out before last week's Berlin Open on the surface, saying she wanted more time to recover and prepare for Wimbledon.
The 19-year-old matched her compatriot early in the opening set before losing seven straight games in hot conditions in central Germany.
Andreeva was down 4-0 and 40-15 in the second set but fought off the break point and won three straight games to elbow her way back into the match.
But 31-year-old Alexandrova, ranked 19th in the world, steadied herself to serve out the set and win the match in one hour and 28 minutes.
Alexandrova will face Japan's Naomi Osaka in the quarter-finals.
Fourth seed Karolina Muchova cruised into the quarters with a dominant 6-1, 6-1 win over Irina-Camelia Begu.
She will face Dane Clara Tauson, who beat China's Zheng Qinwen 5-7, 6-4, 6-2.
Ukrainian world number eight Elina Svitolina pulled out of the tournament on Wednesday, saying Tuesday's last-16 win over Liudmila Samsonova took a "little bit more than expected out of my body".
Svitolina was scheduled to play China's Wang Xinyu in the quarter-finals on Thursday.