Attorney General Arely Gomez didn't release the suspects' names, but she told reporters that authorities had dismantled the group that "planned, organized and effected the escape" of Guzman.
Among those detained was Guzman's brother-in-law, she said, who allegedly organized and supervised the construction of the tunnel Guzman used to get out.
Official: Guzman won't escape from justice
Nicknamed "Shorty" for his height, Guzman had broken free once before from a maximum-security prison, in 2001, reportedly hiding in a laundry cart.
Government officials hailed his capture in 2014 as a sign they were winning the drug war. His July escape sent authorities scrambling and sparked widespread criticism of corruption in Mexico
Since the brazen breakout, authorities have stressed that won't stop until the Sinaloa cartel chief is behind bars again.
It's a message Gomez repeated on Wednesday, telling reporters that 34 people have been detained so far and investigators haven't lost sight of their No. 1 target.
"We will keep working together until we achieve his recapture," she said. "Guzman managed to escape from prison, but neither he nor those who helped him will escape from justice."
Pilot, tunnel supervisor detained
In addition to Guzman's brother-in-law, Gomez announced Wednesday that five others had also been detained:
-- The main operator and organizer of the escape, who, according to Gomez, worked "under the protection of the coordination of the legal defense" of Guzman and "used that cover" to regularly enter the prison, receive instructions and give updates about the escape plan.
-- A longtime pilot for the Sinaloa cartel, who allegedly participated in the escape and in drug trafficking operations.
-- The person who allegedly coordinated the purchase of the property where the tunnel out of the prison ended.
-- The person who allegedly organized and directed the construction of the prison tunnel and other tunnels along the U.S.-Mexico border.
-- The person who allegedly handled the transfer of the property where the tunnel was built.
Gomez also released new details about where Guzman went after he broke out.
Once he made it through the milelong tunnel, Gomez said, Guzman traveled north about 140 kilometers (87 miles) on land to the city of San Juan del Rio, where two small planes were awaiting his arrival and took off from an airstrip.