Maduro said the assistance was part of a plot to strengthen the opposition and blocked it from entering.
The South American nation's socialist government ordered the borders with Aruba, Bonaire, Curacao, Brazil and Colombia closed in February as the opposition tried to deliver food and medical supplies into the country. Maduro denied that a humanitarian crisis exists in Venezuela and suggested that aid efforts are part of a U.S. plot to orchestrate a coup.
On Friday, UN aid agencies said four million Venezuelan refugees and migrants have fled the economic and humanitarian crisis in their homeland - all but 700,000 of them since the end of 2015.
Following the visit, the Colombian president, whose country has received 1.3 million refugees from Venezuela, said he hoped Jolie's visit would raise attention to the seriousness of the migration crisis.
In February, the Francisco de Paula Santander Bridge over the Tachira River, which connects Colombia to Venezuela, became the scene of a showdown between opposition forces trying to make way for the "aid" trucks and the National Guard.
The once-wealthy oil nation is now facing severe shortages of basic goods and hyperinflation that is expected to surpass 10 million percent this year, according to a recent International Monetary Fund estimate.
"These alarming figures highlight the urgent need to support host communities in the receiving countries", said Eduardo Stein, joint UNHCR-IOM Special Representative for Venezuelan refugees and migrants. The chaos has been further aggravated by US sanctions on Venezuelan oil exports and has forced an estimated 5,000 people to leave the country each day, according to the United Nation's refugee agency.
"The president and I spoke of the risk of statelessness for more than 20,000 Venezuelan children", Jolie said.
Speaking in Colombia, the 44-year-old star urged the worldwide community to come to the aid of the South American county before adding that 20,000 Venezuelan children were at risk of being without basic citizenship rights.
Maduro accuses his foes of plotting with Washington to bring about a coup.