Patrick Rock, a special adviser on policy, was arrested by detectives from the National Crime Agency (NCA) over a "potential offence relating to child abuse imagery", a Downing Street spokeswoman said.
He was arrested at his home on February 13 and officers were given access to all IT systems and offices at Number 10, she added.
In a statement, Downing Street said: "On the evening of February 12 Downing Street was first made aware of a potential offence relating to child abuse imagery.
"It was immediately referred to the National Crime Agency (CEOP). The Prime Minister was immediately informed and kept updated throughout. Patrick Rock was arrested at his home in the early hours of February 13, a few hours after Downing Street had reported the matter.
"Subsequently, we arranged for officers to come into Number 10 and have access to all IT systems and offices they considered relevant.
"This is an on-going investigation so it would not be appropriate to comment further, but the Prime Minister believes that child abuse imagery is abhorrent and that anyone involved with it should be properly dealt with under the law."
The spokeswoman confirmed Mr Rock - who was deputy head of Downing Street's policy unit - resigned on February 12.