Security officials detained the suspects in two operations in the central state of Puebla, the attorney general's office said in a statement.
A lawyer for Telmex had accused them of working for companies which dealt with copper extracted from cables stolen from Mexico's main telephone company,it said.
The "constant theft caused interruptions in telephone services in different municipalities of the state," it said.
Authorities also confiscated around 2.5 metric tons of copper cables, bullet cartridges and vehicles in the operations.