Pompeo will assist "a smooth and orderly transition process" to President-elect Joe Biden that includes identifying officials who will stay on temporarily as the new administration takes charge, State Department spokeswoman Morgan Ortagus said.
"As a result, we are cancelling all planned travel this week, including the Secretary's trip to Europe," she said in a statement.
The State Department announced Monday that Pompeo would pay a short visit to Brussels to meet NATO Secretary-General Jens Stoltenberg and Belgian leaders.
The cancellation comes as Democrats push Vice President Mike Pence to remove Trump through the 25th Amendment for inciting a deadly storming of the US Capitol last week by his supporters, who sought to overturn Biden's victory.
Pompeo, who after the election suggested that Trump would stay on for a second term, has condemned the violence but resolutely backed the president.