"I'm satisfied with the draw," Sharapova said. "I wanted to play in the first match and I'm happy I will."
Sharapova was last week's Aussie runner-up to No. 1 Belarusian star Victoria Azarenka. The currently third-ranked Sharapova is a three-time Grand Slam champion and former world No. 1.
On Sunday, the reverse singles will pit Sharapova against Suarez Navarro and Kuznetsova versus Soler-Espinosa, while the doubles call for a Russian tandem of Ekaterina Makarova and Nadia Petrova to take on a Spanish duo of Nuria Llagostera Vives and Arantxa Parra Santonja.
The Russians, captained by Shamil Tarpischev, were last year's Fed Cup runners-up to the Czech Republic.
Russia is 5-1 all-time versus Spain in Fed Cup play. The Russians own four titles, while the Spaniards are five-time winners of the coveted chalice.
The winner here will meet the Belgium-Serbia victor in the semifinals in April.