The discovery comes a day after the match was cancelled when a bomb was detonated close to the players' bus.
Two suspects have emerged after the initial bombing.
One has been arrested.
German police have said the objects found by an exit of the stadium are being examined – just moments after Dortmund lost 2-3 to Monaco.
Earlier this evening Borussia Dortmund fans put on a show of defiance on Wednesday as they poured into their home stadium for their match against AS Monaco, after the postponement.
Borussia Dortmund stadium surrounded by police over fresh attack fears
Police snapped outside Borussia Dortmund's training ground after bus attack
Wed, April 12, 2017
There was a strong police presence outside Borussia Dortmund's training ground this morning in the aftermath of the attack on their team bus last night
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Police were pictured outside Dortmund’s training ground after the bus attack
But the sea of fans, decked out in the team's black and yellow colours and accompanied by an increased police presence, could not quite shake off a feeling of shock after Tuesday's attack in which Spanish defender Marc Bartra was injured.
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He was treated for a broken wristbone and had shrapnel in his arm.
Chancellor Angela Merkel praised Dortmund fans for taking in AS Monaco supporters overnight so they could stay on for the postponed match.
A spokeswoman for the Federal Prosecutor's Office, which handles probes into suspected terrorism, said the explosive devices had contained strips of metal
Borussia Dortmund take on Monaco 24-hours after bus bombed
Spokeswoman Frauke Koehler said investigators had found three letters near the scene, all with the same content suggesting a possible Islamist motive.
She said the letters referred to the use of Tornado reconnaissance planes in Syria, which Germany has deployed as part of the military campaign against Islamic State, and also called for the closure of the U.S. military base at Ramstein in western Germany.
Investigators had identified two suspects from the "Islamist scene", searched their apartments and detained one man, she said.
The solidarity prevailed just hours later before kick off as the two teams entered the stadium and prepared for the quarter-final match, with fans from the two teams drinking together and hugging each other.
"We're not just playing tonight for ourselves. We're playing for everyone!" Borussia Dortmund's managing director Hans-Joachim Watzke said in a tweet.
Police line the outside of the Borussia Dortmund stadium