She was immediately tackled by three security agents and arrested, while a shaken Zeman was escorted from the room.
Under the constitution, the president has another attempt and Zeman said he would tap Babis again, should he fail to win confidence.
He leads eight other candidates, with around 41.3 percent of the votes, according to the results from half of the districts.
"I congratulate Jiri Drahos for this attractive second place", he added.
A win by any of Zeman's main rivals could mean that voices from the Czech leadership may shift closer to the European Union mainstream, in contrast to ex-communist neighbours such as Poland and Hungary, whose governments have clashed with Brussels.
He also has harsh anti-Muslim views, having once called the 2015 migrant crisis "an organised invasion" of Europe and insisted Muslims were "impossible to integrate".
"We are in a situation where if everything goes badly we could be faced with regime change, and though not another dictatorship, we could still perhaps become an illiberal democracy", said political analyst Jiri Pehe, director of New York University in Prague.
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Eight have pleaded guilty and were ordered to pay more than $2.6 million in back wages, and the ninth was arrested in November. He said there would be more employment audits and investigations, though there is no numerical goal.
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Chelsea will take on Coutinho's new side in the Champions League round of 16 but the Brazilian will be cup tied for Barcelona . I just want him to be one of the best in the world and enjoy what he can do". "We only have to carry on".
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But Lt Col Conricus said this did not mark "more of the same" since it involved the most advanced technological means Israel has deployed.
"The president should work to unite society".
"It is a clash between. the post-communist part of society represented by Zeman and the other part, say, modern, pro-Western, which simply doesn't want this president any more".
ANO topped the vote, scoring 78 of 200 parliamentary seats campaigning on an anti-corruption and anti-euro ticket.
He has the support of Czech Prime Minister Andrej Babis.
In the 1990s, Zeman led the Czech Social Democratic Party (CSSD) out of the political wilderness and into power, cementing its position as the country's leading left-of-center party over the past two decades.
If the caretaker prime minister fails to win a vote of confidence before Zeman's term ends in March, the next president may force snap legislative elections. Drahos said he needed to boost his visibility outside the capital - the only region he won - and would focus on that ahead of the second round.
The turnout of the vote was 61.74 percent.
Polling stations reopened at 0700 GMT and will close at 1300.