Bobrova said a drugs test showed she had traces of Meldonium in her blood, which is used to treat chest pains, though it can increase fitness levels and is on the World Anti-Doping Agency's banned list.
"Unfortunately we will be unable to take part in the World Championships in Boston," Bobrova was quoted as saying.
"The Russian Figure Skating Federation recently received a letter from the International Skating Union, which stated a drugs test I had taken after the European Championships showed traces of Meldonium," the 25-year-old said.
Bobrova also announced that she will not seek to have her "B" sample tested.
The pair's coach, Alexander Zhulin, said a large amount of the banned substance was found in Bobrova's system and said she may have taken the drug without knowing about it.
"Ekaterina is a sober and wise woman," he told R-Sport.
"She would never have done this in her life and the dose as far as I am concerned is quite big. This entered into her system during the final 24 hours of the European Championships. I am in shock and even demoralized about what has happened," Zhulin said.
Bobrova and Solovyov won a gold medal at the 2014 Winter Olympics in Sochi, Russia, in the team discipline.
In January, the pair won bronze at the European Championships in Bratislava.
They will be replaced by Alexandra Stepanova and Ivan Bukin for the event in Boston, which takes place from March 28 until April 3.
Russia was suspended from athletics in November after a special commission of WADA exposed widespread state-sponsored cheating and corruption. It will be allowed to compete in August's Rio Olympics only if it convinces investigators it has met clearly defined standards.
(Reporting by Dmitriy Rogovitskiy; Editing by Alison Williams)
