The Cubs will not send out an official announcement until Saturday, when they're also expected to announce their corresponding move.
"The MRI, they say it's mild to moderate," Soto said. "The doctors say that it's not even close to the worst you could have, so that's a good sign."
Soto injured himself during batting practice on Wednesday.
"First round [of batting practice], we're fine, taking the ball the other way and keep hitting the ball through the middle and I felt like something grabbed me," Soto said. "I came out of the cage. By the second round I went in there again, I just couldn't do it anymore."
If the team is not able to find a catcher on waivers by early Friday afternoon, it likely will promote Chris Robinson from Triple-A Iowa.
The Cubs also recalled right-handed pitcher Jeff Stevens from Iowa, replacing right-handed pitcher Kevin Hart, who was optioned to the minors on Thursday.
The timing is poor for both Soto and the Cubs, who enter a weekend series with the NL Central-leading St. Louis Cardinals.
"We have a huge series starting today and I was really looking forward to being there for my teammates," Soto said. "It's just one of those things you can't really control and hopefully you get back as soon as possible."
Bruce Levine covers baseball for ESPNChicago.com.