Officials say the vandalism happened June 13.
Video captured from a cell phone shows a young man using spray paint and a stencil to deface the artwork.
A spokesman for the Menil Collection said today that restoration work on Picasso's "Woman in a Red Armchair" has been "going very well" and the damage appears to have been caught in time. Musuem officials were able to clean and restore the painting almost immediately.
Houston police are still investigating, and no charges have been filed in the case.
Police spokeswoman Jodi Silva says investigators are reviewing both surveillance video from the museum, as well as a cell phone video taken by a witness and later posted on YouTube. That video is posted below and contains graphic language.
This video contains GRAPHIC LANGUAGE.