The 17th-ranked Safarova is 3-2 against the 12th-ranked Ivanovic, who is former No. 1.
"It would be great to start with a lead," Safarova said at the draw ceremony at Prague City Hall. "That's what I'm going to try and I'm looking forward to."
Eighth-ranked Petra Kvitova, who led the Czechs to a 3-2 victory over Russia last year, will play Jelena Jankovic -- another former No. 1 -- in the second singles match on indoor hard courts at the O2 Arena on Saturday.
Kvitova has recovered in time from a viral illness that forced her to pull out of the WTA Championships last week.
"I feel very good. I practiced yesterday one hour and something and it was quite OK," Kvitova said. "It's a big end of the season, we play at home and I play for the team, for the Czech Republic and that makes me strong."
Both Kvitova and Jankovic have been unbeaten for the last two years in Fed Cup singles. Kvitova won their only previous encounter last year at a WTA event in Linz, Austria.
"It's very special occasion for all of us," Jankovic said. "We're all here to do our best."
Serbia has had its best Fed Cup season since the country became independent. It recorded victories in the World Group with away wins over Belgium and Russia to reach its first final.
In Sunday's reverse singles, Kvitova plays Ivanovic before Safarova takes on Jankovic.