The child had been struggling to stay above water while crossing a pond in the Rio Grande Valley on Saturday.
Footage obtained by Fox News shows the agent in the water pulling the child to safety.
Meanwhile, the Border Patrol detained five Mexican nationals Tuesday morning in La Joya, west of McAllen.
Fox News’ Griff Jenkins told “America’s Newsroom” that he and a producer were filming in the area when a group of seven people emerged from the brush after crossing a river and ran toward him and his producer’s vehicle.
Jenkins says five were caught – but agents are still searching for two.
On Monday, within hours of arriving in the area, more than 200 migrants hailing from countries including Honduras, Guatemala, El Salvador and Ecuador, were seen surrendering to the Border Patrol, Jenkins added.
“There is a crisis right now at the southern border … the numbers show it, as far as illegal crossings, as far as criminal activity, drugs, criminal apprehensions,” Texas Department of Public Safety Lt. Christopher Olivarez told Fox News on Monday.