The top two seeds were hoping for a grass-court run ahead of The Championships in SW19, but suffered surprise defeats to unseeded opponents.
Last year’s Wimbledon champion Kvitova, seeded second at the AEGON International but the world number four, lost 7-5 6-4 to world number 48 Ekaterina Makarova.
Makarova, who won the Eastbourne tournament in 2010, missed a chance to close out the match as Kvitova finally cut out the errors and hit a flurry of winners to win a break back, but the Russian 24-year-old was not to be denied.
Makarova now meets British hope Laura Robson, who came from a set down to beat Spain’s Maria Jose Sanchez Martinez 3-6 6-2 6-2.
Robson's compatriot Heather Watson beat Hungary's Greta Arn 6-3 6-4 and will face Czech star Lucie Safarova after she beat another Hungarian, Timea Babos, 3-6 6-3 7-6.
The top-seeded Pole Radwanska suffered a comprehensive defeat to Bulgaria’s Tsvetana Pironkova, who cruised to a 6-2 6-4 victory.
World number 40 Pironkova is up against Stephanie Dubois after she beat Carla Suarez 6-4 6-4.
She faces South Africa’s Chanelle Scheepers for a place in the third round.
Klara Zakopalova was also victorious on Tuesday, although she was pushed hard by China’s Jie Zheng in a match that finished 6-3 4-6 6-3.
The Czech is up against ninth-seeed compatriot Petra Cetkovska, who beat another Czech Andrea Hlavackova 3-6 6-2 6-1.