In a statement, the owners of the attraction say the three people were taken to a hospital but the extent of their injuries was unknown.
"Our thoughts and prayers continue to be with all who were affected, including the first-responders," owners Mary Kellogg Joslyn and John Joslyn said.
"Needless to say, we never would have expected an incident like this to occur as the safety of our guests and team members is always top of mind," they said.
The Titanic Museum says it allows "passengers" to experience the environment of the Titanic including touching "a real iceberg."
Other attractions allow them to reach their hand in 28-degree water, walk the grand staircase, and try to stand on a sloping deck. The attraction also hosts weddings.
The museum reopened on Tuesday but the museum anticipates it will take at least four weeks for the iceberg to be rebuilt.
The owners say they are reevaluating our quality and safety guidelines and will make any necessary modifications.