Two U.S. Marines died on Friday in the assault on Camp Bastion in Helmand Province.
The Taliban said it carried out the attack to avenge an anti-Islamic film and because the prince is serving on the base. The film mocks the Prophet Muhammad and has sparked anti-American protests in many countries.
British officials said the prince's deployment was carefully planned and every measure is being taken to mitigate all threats.
Prince Harry's status as third in line to the throne has complicated his military career. He is serving a four-month combat deployment as a gunner on an Apache helicopter. Harry, who turned 28 on Saturday, is set to start flying Apache missions this week. This is his second tour in Afghanistan.
The Associated Press contributed to this report.