Police said the home, abandoned when they arrived, had been occupied for about four months. Its former occupants were considered suspects, but there were no immediate arrests.
Officials with the armored car company -- Transnacional Transporte de Valores e Seguranca Patrimonial Ltda -- told officers that 10 million reals ($5.9 million) were missing, according to the statement.
Globo TV's G1 Web site reported that electricity was cut off to the company's office and some security cameras were not on when the theft happened, but authorities did not immediately confirm that.
The heist occurred on the last weekend of the football season, when the league championship and relegation matches had people nationwide glued to their televisions.
A security guard at the building heard a loud noise about 5 p.m. Sunday, but figured it was from fireworks that sports fans had been setting off throughout the afternoon, the newspaper O Estado de S. Paulo reported.
The newspaper said thieves left behind sacks of coins in the tunnel, and police found a map of the tunnel and bags of dirt in the house -- presumably from the excavation. A Christmas tree inside the house was visible from outside.
Firefighters who inspected the tunnel Monday said it was about a yard (meter) high and a yard (meter) wide, G1 reported.
Two years ago, thieves used dynamite to blow up a safe and steal nearly $10 million from the office of another money transport company in Sao Paulo, South America's largest city and Brazil's hub of finance and commerce.
In 2005, about 10 suspects tunneled under a city street and stole more than $70 million in cash from a central bank branch in the northeastern city of Fortaleza. It was the world's biggest heist ever until more than $90 million was taken from a security warehouse in London a year later.
