The money is believed to have been stolen after June 20 and the theft was reported on Friday September 8.
Police refused to say how much money was reportedly taken.
A Met Police spokesman said: "An investigation into the alleged theft is now being carried out.
"Steps have been taken to review the security of all the flats within Grenfell Tower and some changes immediately put into place."
At least 80 people died and hundreds more were left homeless when flames engulfed the 24-storey block on June 14.
A total of 58 people have been confirmed dead as inquests into the deaths begin.
The latest tribute paid to a victim was Biruk Haftom , a 12-year-old described as "a loving, pure-hearted boy, wise beyond his years".
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