The officer died in April 1984 after shots were fired from the Libyan Embassy in London at a protest outside.
A man in his 50s, arrested in November 2015, was released on Tuesday due to "insufficient admissible evidence", Scotland Yard said.
PC Fletcher's family said they were "deeply disappointed and frustrated".
The Met said its investigation had identified enough material to identify those responsible for Fletcher's murder if it could be presented to a court.
"However the key material has not been made available for use in court in evidential form for reasons of national security," a spokesman said.
"Therefore, without this material and following a review of all the evidence that was available to prosecutors, the Crown Prosecution Service - who we worked closely with throughout - have informed us that there is insufficient admissible evidence to charge the man."
PC Fletcher, 25, had been policing a small demonstration outside the Libyan People's Bureau in St James's Square against the regime of Col Muammar Gaddafi.
She was one of 30 unarmed police officers at the scene when shots were fired from the first floor of the diplomatic mission.
In a statement, her family said they were satisfied the Met had "left no stone unturned" in its pursuit of justice but said they had "hoped for some closure".
"We are deeply disappointed and frustrated that a prosecution cannot proceed at this time. We had hoped that the latest turn of events would finally lead to some closure," it added.
The Met said the investigation would never be closed but added the likelihood of finding further evidence, in Libya or elsewhere, was low.
Assistant Commissioner Mark Rowley said: "I regret that we have not been able to deliver the justice that the victims and their families deserve.
"Our thoughts today are with PC Fletcher's family and all those affected by the events of that day in 1984."
A man arrested on suspicion of conspiracy to murder PC Yvonne Fletcher three decades ago has been released without charge.