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According to Pan-American Health Organisation figures, the country is second only to Brazil in infection rates, Alejandro Gaviria told journalists on Wednesday.
"We expect an expansion similar to what we had with the chikungunya virus last year, to finish with between 600,000 to 700,000 cases," he said.
Some 560 pregnant women are among those infected, the minister said, though so far no cases of newborns suffering from microcephaly, a congenital defect caused by Zika, have been registered in the country.
The government is advising Colombian women to delay becoming pregnant for six to eight months in a bid to avoid potential infection.
The US Center for Disease Control and Prevention last week warned pregnant women to avoid travel to 14 countries, including Colombia, which borders Brazil, and territories in the Caribbean and Latin America affected by the virus.
Alarm over the virus comes two weeks before nationwide Carnival celebrations - a highlight of Brazil's tourism calendar - and nearly 200 days before Rio de Janeiro hosts the opening ceremonies of the 2016 Olympics, the first in South America.