Bale was forced off at half-time against Villarreal on Wednesday as Madrid were held to a 2-2 draw.
But the club have confirmed the problem is minor.Grade-one tears are the least severe of the three classifications.
A statement read: "After tests carried out today on our player Gareth Bale by the medial services of Real Madrid, he has been diagnosed with a grade-one injury in the left calf."
Bale will miss the La Liga game against Real Sociedad on Sunday and is unlikely to be risked against Leganes in the first leg of the Copa del Rey on Wednesday.
Madrid will hope to have him back later this month, however, with league games against Real Betis, Sevilla and Espanyol to come.
"We think the injury is not too serious," Solari said at a press conference earlier on Saturday. "He will go through tests today and we all hope he is back with us quickly."
Expectations were high for Bale this season following the departure of Cristiano Ronaldo last summer, but the Welshman's rhythm has been disrupted by fitness issues.
He has made 22 appearances for Real but played 90 minutes only five times.
Bale's absence could mean a reprieve for Isco. He has been out of favour since Solari took charge but replaced the Welshman against Villarreal.
Speaking ahead of the match on Sunday, Solari seemed positive about the prospect of Isco coming in.
"Isco is so good he can play wherever, in any position on the pitch," Solari said.
"Sometimes it's not all about speed. You can be effective with your creativity, imagination and technical ability. Every player has different characteristics."
The draw against Villarreal leaves Madrid fourth in the table, seven points adrift of leaders Barcelona. Madrid have 30 points, which is the club's lowest total after 17 games in 13 years. At one stage this season they were as low as ninth.
Solari, however, insisted "you cannot underestimate draws", and added: "The important thing is to keep climbing the table. To get from ninth to fourth has been difficult and we want to keep going. La Liga is long and in times of adversity, you see character."
Marcelo has been among those criticised, with the defender at fault for Villarreal's opening goal in midweek. He has returned after suffering a hamstring injury in October.
"Marcelo has had a very difficult injury and it has not been easy for him," Solari said.
"He is getting his rhythm back and he is a fundamental player for the team and the club. Over a season you can have good and bad games, but we must look after Marcelo."
As well as Bale, Marco Asensio, Marcos Llorente and Mariano Diaz are all recovering from injuries and expected to miss the game on Sunday.AFP