Israeli defence officials said it was a "pinpoint'" operation aimed at fighters but medics said the baby was killed in the crossfire and at least eight fighters and three civilians were wounded.
The armoured column entered Gaza through the Kissufim crossing. Witnesses said that, during the clashes, Israeli tanks fired shells and helicopters fired missiles.
Talks in limbo
The operation came as the visiting US secretary of state failed to win a public commitment from the Palestinian president on Tuesday to resume negotiations towards a peace treaty with Israel.
Mahmoud Abbas, who on Sunday suspended negotiations in protest against the Israeli offensive in Gaza, urged Israel to halt military operations to create the atmosphere for talks.
Condoleezza Rice told a joint news conference with Abbas in the West Bank city of Ramallah that "we look forward to the resumption of those negotiations as soon as possible".
But Abbas sidestepped a question on when talks might get under way.
"I call on the Israeli government to halt its aggression in order that we can afford the necessary atmosphere to conduct the negotiations," he said, without setting any timeframe for their resumption.
Rice blamed Hamas for obstructing talks and having "no interest in peace".
But while she said the "US understands the right of Israel to defend itself" against rocket attacks, she said many innocent people had been caught in the crossfire.
"Israel needs to be very cognisant of the effect of its operations on innocent people," she said.
Israel had pulled back its troops from the Gaza Strip on Monday, before Rice's arrival in the region.
But a senior Israeli official said that the pull-back would only be a "two-day interval" during her visit.