"I'm satisfied with the draw," Sharapova said. "I wanted to play in the first match and I'm happy I will."
It will be Sharapova's third appearance for Russia. The Australian Open runner-up won both her singles matches against Israel in 2008 but lost in opening singles against France last year.
Russia is the clear favorite to win but Sharapova refused to underestimate the opponent.
"Last season, we were favorites against France at the same stage of the competition but fell 2-0 down after the opening singles," Sharapova said. "We were lucky to win in the end."
In Sunday's reverse singles, Sharapova will play Suarez Navarro, while Kuznetsova will take on Soler-Espinosa. In the doubles match, the Russian pair of Nadia Petrova and Ekaterina Makarova will play Nuria Llagostera Vives and Arantxa Parra Santonja.
The reverse singles and doubles pairings in the best-of-five series on the indoor hard court at the Olympic indoor stadium can be changed depending on the results of earlier matches.
Russia has won the Fed Cup title four times since 2004 and is 5-1 against Spain, which won the title five times between 1991 and 1998.
The winner will play Belgium or Serbia in the semifinals April 21-22.