Police in Calcutta identified the local men as Tauseef Rahman, a clerk, and Mukhtar Ahmed, a street vendor and taxi driver. Ahmed was arrested in New Delhi.
Senior police official Javed Shamim told reporters the men were arrested late on Friday: "They are in police custody and being questioned."
The arrests, believed to be the first since the attack, came after investigators tracked down the identities used to buy the SIM cards recovered from the dead gunmen.
Senior police official Rajeev Kumar said Tauseef Rahman is believed to have bought the SIM cards using the identities of dead people, before selling them on to Mukhtar Ahmed. Both have been charged with forgery.
SIM cards can easily be obtained without genuine ID on the black market in Calcutta and most other Indian cities.
A group of about a dozen gunmen carried out a series of coordinated attacks on November 26-29 in Mumbai, India's financial capital, killing at least 188 people including 26 foreigners.
Indian authorities have accused the Pakistani-based militant group Lashkar-e-Taiba of training the terrorists and planning the attacks.