Ivo Josipovic topped the first round of the elections, securing 38.46% of the ballots, just ahead of Grabar-Kitarovic with 37.22%, preliminary data from the State Electoral Commission showed on Monday.
Some 3.79 million Croatians were eligible to vote in the presidential elections. The turn out was at 47.14%.
The run-off is set for January 11.
Josipovic is supported by the ruling centre-left SDP which is struggling to turn around the country's ailing economy amid a multi-year recession.
The other two presidential candidates, independent human rights activist Ivan Sincic and the head of the conservative Croatian Dawn-Party of the People, Milan Kujundzic, secured 16.42% and 6.3%, respectively, of the votes at the Sunday polls.
The last presidential elections in Croatia were held in December 2009. Josipovic was sworn in in February 2010.
The Croatian president is elected for a five-year term.