Portugal right-back Pereira had an operation on Thursday after sustaining the injury during last Sunday's friendly win against Sevilla.
Rodgers also confirmed Harvey Barnes will miss Sunday's Premier League opener against Brentford at the King Power Stadium through injury.
The Foxes boss told a press conference: "It was looking really good, but we've picked up injuries against Sevilla.
"Sadly Ricardo Pereira will be out for up to six months with a ruptured Achilles. A lot of our game idea was about our full-backs and him in particular. He was looking so good.
"It's a massive blow to him. He had his operation last night and he'll recover now, get strong again and come back better I'm sure."
It is a second major injury setback for Pereira since he joined the club from Nice for £21.8million in 2018, having been sidelined for nine months after damaging knee ligaments in March 2020.
Rodgers said winger Barnes could be out for "a few weeks" due to a knee injury.
"Hopefully he won't be too long and he can come back and pick up where he left off," Rodgers said.
The Foxes remain the only top-flight club yet to complete a summer signing and Rodgers does not expect to strengthen his squad in the current transfer window.
Kasper Schmeichel ended his 11-year spell with the club by joining Ligue 1 side Nice earlier this week, but Rodgers said Danny Ward and Daniel Iversen will now vie for the number one jersey.
When asked about possible recruits, the Northern Irishman said: "As things stand, I believe not.
"I mentioned that before, there's nobody imminent coming in. The concentration has purely been on the players who are here. I think we can do well.
"I felt this was a time we would need to improve, but I respect the club's position. The club have been outstanding in supporting me. This time, I need to support them.
"It's unfortunate. I don't need to fight with anyone. I would have loved to improve the squad and there is time until the end of August if things change."
Rodgers remains hopeful the club can fend off interest from rival clubs in key players Wesley Fofana, James Maddison and Youri Tielemans.
Newcastle have had a £40million offer for Maddison turned down while Chelsea and Arsenal have been linked with Fofana and Tielemans respectively.
Rodgers added: "These players are not for sale. We need to move players out, but it's not getting rid of everyone and certainly not our best assets.
"It's something the club are very strong on. James and Wesley are training very well and working hard for our game on Sunday."