The senior west London coroner Chinyere Inyama "inadvertently disposed" of a 30-page document of evidence against the chief suspect Arnis Zalkalns in November, police said.
The Metropolitan Police Service (MPS) tried to recover the file but concluded it had probably been destroyed.
Alice went missing in August and her body was found in a river in September.
Her family said they were "extremely concerned, bewildered and angry" that highly sensitive information about Alice had been lost.
The force said the search for the missing 14-year-old was the largest investigation it had undertaken since the 7 July 2005 bomb attacks in London. Her body was found in the River Brent on 30 September 2014.
The body of Arnis Zalkalns, 41, from Latvia, was found on 4 October, decomposed in woodland in west London.
A post-mortem examination found he died from hanging.
The following month, a copy of the police file against him was lost.
Alice's family said: "We have looked to the police and coroner to help us through our awful loss. Yet now we learn they - either independently or together - have withheld from us the loss of this terribly sensitive information about Alice.
"We are extremely concerned, bewildered and angry, and we have asked for a full written explanation as to what exactly happened and why we were not told."
A spokesman for the Met said: "In November 2014 the MPS was informed by HM Coroner, London West, that he had inadvertently disposed of a single document relating to the police evidence against Arnis Zalkalns.
"An investigation to recover it was undertaken. This concluded that it was highly likely it had been destroyed as waste."
Police said details of the evidence against Zalkalns was provided to the media in January with the agreement of the CPS and the coroner.
The coroner was given the file to assist in his preparations for the inquests into Alice Gross and Zalkalns' deaths.
The Ministry of Justice said: "This clearly appears to be a troubling incident. A full investigation is now under way."
A copy of the police investigation file into the murder of schoolgirl Alice Gross was left by a coroner on a train.