That was slightly higher than a Reuters forecast, which saw inflation at year-end in Latin America's second biggest economy accelerating to 6.75 percent from 6.63 percent in November.
Consumer prices rose 0.59 percent in December, according to non-seasonally adjusted figures.
The core index, which strips out some volatile food and energy prices, rose 0.42 percent during the month. Inflation surged after the liberalization of gasoline prices at the start of last year, though central bank governor Alejandro Diaz de Leon said on Sunday the rate should slow in January as that factor fades from the consumer price index.
Mexico's central bank targets inflation of 3 percent, and its board said recently it expects the rate to reach that goal slower than it had previously predicted.