The policy promises to create ill-will after officials last weekend doubled the price of Wednesday tickets after Federer's late decision to play in Rome.
"If a session is postponed or cancelled due to weather or acts beyond our control, the Tournament Committee will attempt to accommodate the ticket holder at a subsequent session," the website statement read.
"In the event of rain during play the Committee will determine whether a session is completed. However, no refunds will be given."
The Swiss icon last appeared at the Foro Italico in the 2016 third round, losing to Dominic Thiem.
He was due to begin on Wednesday against Portugal's Joao Sousa.
Federer, a four-time finalist in Rome, returns to Italy after skipping the clay season for the last two years in order to concentrate on his grass game.
"We want to reward fans who had bought tickets before they knew Federer would play," the Italian Tennis Federation explained.
When informed of the decision on Tuesday during a media event, Federer did not seem particularly impressed.
"I heard some fans clearly were not happy about it. That's obviously disappointing to hear," the 20-time Grand Slam champion said.
"They made it in a way like they rewarded the fans who bought tickets earlier, which is sort of strange, but okay.
"I just really hope it doesn't take away the fact I'm really happy to be here.
Due to the rain and wintery temperatures in what is normally a warm and pleasant period of the year in the Italian capital, the order of play was re-arranged and reduced, with starting times regularly delayed as the day dragged on.
Djokovic was facing Canadian Denis Shapovalov while Nadal was to play France's Jeremy Chardy.
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