The tests were carried out on Saturday at SpaceX's test stand in Cape Canaveral, located in the southeastern US state of Florida.
"The initial tests completed successfully but the final test resulted in an anomaly on the test stand… Ensuring that our systems meet rigorous safety standards and detecting anomalies like this prior to flight are the main reasons why we test… Our teams are investigating and working closely with our NASA partners", a SpaceX spokesman told the media outlet Space News.
"We will work closely to ensure we safely move forward with our Commercial Crew Program", Bridenstine wrote on Twitter.
Space News reported that on Saturday afternoon eyewitnesses had seen a dark cloud from somewhere near the US Air Force facility in Cape Canaveral.
Crew Dragon, also known as Dragon 2, is a reusable spacecraft designed as a successor to the Dragon space freighter. It is expected to perform its first manned test mission in July, while problems during tests could result in a change of plans.