Ramos returned from a knee issue ahead of the international break and scored for Madrid as it knocked Atalanta out of the UEFA Champions League.
However, he then played just 50 minutes across two appearances for Spain in FIFA World Cup qualifying and complained of a calf problem after a short cameo at home to Kosovo.
Madrid has not confirmed the anticipated length of Ramos's lay-off, but a return in time to face Liverpool in the UEFA Champions League quarter-finals and Barcelona in LaLiga appears unlikely.
Los Blancos hosts Liverpool on 7 April (AEDT), with a second leg eight days later sandwiching a critical home El Clasico.
Given Ramos has appeared just 20 times for Madrid in all competitions this season, questions might be asked of his involvement for Spain.
But Zidane said on Saturday (AEDT): "No one has the blame here – not Spain, not Real Madrid. This is just football.
"Unfortunately, these things happen; it's happened before, not just to us but to a lot of other teams as well.
"It's true that, this part of football, we don't like it, of course, but these things happen. We have to accept this, but no one is to blame here.
"What we want for Sergio is that he recovers as quickly as possible. We know the player and captain he is. We know that he always wants to be available and playing.
"This has hurt us a little bit and we hope he recovers quickly."
Ramos's absence for the two legs against Liverpool would appear particularly costly as Madrid has lost seven of the 10 UEFA Champions League games he has missed since the end of the 2017-2018, the season in which it was most recently crowned European champion and also when Cristiano Ronaldo departed for Juventus.
The centre-back has made 14 European appearances in that time and contributed to 10 wins, losing only once, while Los Blancos concede only 0.9 goals per game with him in the side – down from 1.9 without him.
But Zidane was not looking as far ahead as an intriguing last-eight tie, as Madrid first faces Eibar on Sunday (AEDT), playing before Atletico Madrid and Barca and able to cut the gap at the top to three points.
"You talk about Liverpool and Barcelona - we have a game tomorrow to play," Zidane said.
"We want Sergio back, we want him to be with us at all times, but right now we just focus on tomorrow's game.
"This is going to mark the path for the rest of the season. We just focus on tomorrow [Sunday AEDT] and that's it. Tomorrow ... we have a game and we have to all be ready, all of us."
Ramos is not Madrid's only injury absentee, either, with Eden Hazard prevented from going away with Belgium and Toni Kroos returning early from Germany duty.
Kroos has been a key man this season, playing 35 games and providing nine assists from 83 chances created, and he is "doing better", Zidane said.
The coach added Madrid is "not going to be silly" with the midfielder but he has trained ahead of the Eibar match.
Hazard, on the other hand, has repeatedly suffered with fitness issues, restricted to only nine starts in 2020-2021 and having a meagre four-goal return.
"Once again, we don't have a plan with Eden," Zidane said. "It's a day-to-day thing, like everything.
"We're not going to force anything because the most important thing is that he's well, that he's recovered. For us, it's bit by bit.
"I'm not going to tell you we'll re-evaluate in a week, a few days, nothing. If it's in a few days, that's good for us; 10 days, okay. We're just going to take it day by day.
"He is with the team now and that's what we want. When he plays, we'll see."