A rise in costs of some food and agricultural products, as well as air travel, fueled inflation in June.
The inflation figure was down from 4.28pc in May and in line with the median forecast of 10 banks, analysts and brokerages, which saw annual inflation of 3.95pc through the end of June.
Mexico's central bank targets inflation of 3pc.
"The large drop in Mexican inflation ... is likely to be followed by another sizeable fall this month.
That should see Banxico inch further towards interest rate cuts, with an easing cycle likely to begin in September," said Edward Glossop, Latin America economist at Capital Economics.
Mexico's economy shrank in the first quarter of 2019, from the previous three-month period and economists have cut their growth forecasts for Latin America's second-largest economy, citing shifts in perception about policy under President Andres Manuel Lopez Obrador.
Mexico's central bank held its benchmark interest rate steady on June 27, although as worries over the economy grew, the board was not united in its decision for the first time since two new members joined at the start of 2019.
In a statement, the Bank of Mexico (Banxico) said one member had voted to lower borrowing costs by 25 basis points, while the rest of the five-strong board opted to hold the overnight interbank rate unchanged at 8.25pc.
Consumer prices rose 0.06pc in June, according to non-seasonally adjusted figures.
The core index, which strips out some volatile food and energy prices, rose 0.3pc during the month, bringing the annual rate to 3.85pc.