Mrs. Trump also represented the administration at the April funeral of former first lady Barbara Bush. "Thank you for so much love and support!" the president said in a Twitter posting on Tuesday.
The First Lady's communication director released a more detailed statement this week, confirming "the procedure was successful and there were no complications".
She underwent the surgery at the Walter Reed National Military Medical Centre in Bethesda, New York Post reported.
"The First Lady looks forward to a full recovery so she can continue her work on behalf of children everywhere", it said.
Melania Trump's spokesperson said the first lady "deserves personal privacy" as she recovers from kidney surgery.
She is the first to go through a serious medical procedure since October 1987 when then-first lady Nancy Reagan had a mastectomy.
An embolization procedure is done to cut off blood supply to a part of the kidney. CNN also reached out to Dr. Jamin Brahmbhatt, a urologist at Orlando Health in Florida, to asked what she would use embolization for.
The procedure is typically done laparoscopically and, according to Friedewald, it typically only causes minor side effects like fever or pain in the kidney or injection site.
But why is the first lady staying in the hospital for so long?
The president started his day by tweeting an update on the first lady early Tuesday morning, saying she would be leaving the hospital in "2 or 3 days".
The White House did not offer any additional details on Mrs. Trump's condition, though Vice President Mike Pence described the procedure as "long planned" as he opened a speech at a Monday evening event celebrating Israel's independence.
The first lady lived full time in NY during the administration's opening months so Barron would not have to change schools midyear. Just last week, she unveiled her "Be Best" campaign, an undertaking which she hopes will help diminish and ultimately end bullying and cyber-bullying.