Rev Nathan Ntege, 55, had been accused of conducting a "matrimonial conveyor belt" of 500 bogus weddings at a church in south-east London.
But his trial fell apart in October when the judge said officers had lied on oath and concealed evidence.
The case against six people accused alongside Mr Ntege also collapsed.
The Independent Police Complaints Commission (IPCC) has said it would examine how three officers handled evidence during the course of their operation and the trial at Inner London Crown Court.
The vicar, from Thornton Heath, had been on trial on 14 counts of facilitating a breach of immigration law and one count of fraud.
The prosecution claimed immigration officials became suspicious because of the "inordinate number" of weddings taking place at the parish church, rising from six a year to six a day.
Judge Nic Madge said the misconduct started when two of the defendants were arrested in June 2011, and had continued "throughout the course" of the trial.
He said: "I am satisfied that this is a case in which there has been both bad faith and serious misconduct on the part of the prosecution.
"I am satisfied that officers at the heart of this prosecution have deliberately concealed important evidence and lied on oath."
Judge Madge also concluded the existence of entries on an investigation log from July 2012 to December 2012 had been concealed and lied about on oath by the officers.
The IPCC said it will investigate the actions of officers "during the course of the operation, which began in 2011,  and during the trial, including their handling of exhibits and documentation, the disclosure of investigative material and evidence given at Inner London Crown Court".
Its investigators are going through over 100 boxes of material, gathering correspondence, trial bundles and transcripts, the IPCC said.
Three officers were suspended following the collapse of the trial.
Three immigration officers are to be criminally investigated after the collapse of a trial over allegedly sham marriages.