Following her triumph in Paris, Krejcikova made it to the round of 16 at Wimbledon only to lose to eventual champion Ash Barty.
Krejcikova will be representing the Czech Republic at the Tokyo Olympics, and is using this home tournament as a warm-up event.
The second seed defeated Shinikova 6-2 6-3 to tee up a second-round tie with Ysaline Bonaventure. With Petra Kvitova already out, Krejcikova will be hoping to seal a third singles title of her career.
Compatriot and fourth seed Marie Bouzkova did not fare well, however, as the fourth seed slumped 3-6 6-4 6-2 to world number 141 Storm Sanders.
Fellow Czechs Katerina Siniakova and Tereza Martincova did progress, beating Jodie Burrage and Samantha Murray Sharan respectively.
While Krejcikova will look to take advantage of a weakened field and prepare for the Olympics in ideal fashion, one player who will not be at the Games is Johanna Konta.
The British number one said on Tuesday she had withdrawn from Tokyo 2020 after testing positive for COVID-19 and seeing her tennis fitness suffer, having also had to pull out of Wimbledon. Konta, who is not in action this week, described the blow as "a heart-breaking reality".
At the Hungarian Grand Prix, third seed Bernarda Pera had to come from behind to beat Julia Grabher – ranked at 201 – 5-7 6-1 6-2.
Pera, who joins a fellow American seed, Danielle Collins, in round two, will next face Anhelina Kalinina.
Irina-Camelia Begu, a finalist in Budapest 10 years ago, will not be making a repeat trip to the title match, the fourth seed losing 6-3 6-4 on Tuesday to Anna Karolina Schmiedlova.
Meanwhile, at the Lausanne Open, fourth seed Camila Giorgi scored a ruthless 6-2 6-0 win over Norway's Ulrikke Eikeri.