Shapps said the new one-hour "lateral flow" test "ultimately could open the way for non-quarantine travel as well".
He was speaking at the Airport Operators Association’s annual conference.
"I want you to know we have been making very good progress on a ‘Test to Release’ programme," he said, adding that this would consist of a single test on arrival "at cost to the passenger" and without any impact on the NHS.
He added: "In addition to the arrivals regime, we are considering self-isolation and testing that can be performed before departure."
Shapps claimed the UK was leading international work to adopt an accepted standard.
The minster was due to take questions, but sent in a recorded message instead, with organisers blaming the outbreak in Denmark for disrupting his schedule.
"Events over the weekend demonstrate the need for vigilance," Shapps said.
He said support for the aviation sector had come via £1-2 billion in furlough payments and another £1.8 billion in corporate financing support.
However, Shapps’ presentation was followed by shadow transport minister Jim McMahon, who said this total only equalled the amount collected in Air Passenger Duty last year.
McMahon said the sector was being overlooked and called for specific support.
"I don’t believe transport has an equal voice around the cabinet table," he said, adding that aviation would be a “foundation for the economy” once the UK emerged from the pandemic.
"Why the government is not supporting it beggars belief," he said.
McMahon said he did not believe APD was a constraint on aviation’s recovery.
"Frankly you can get to most parts of Europe cheaper than London to Manchester by train. I am not convinced it is a barrier, quarantine is the issue."
However, he suggested retaining APD for a limited period of time to reinvest in the sector. "Then you would see that financial support double compared with what Grant Shapps is offering."
McMahon said he was "staggered" the government had not had a more significant role internationally in establishing air corridors with key destinations like Spain.
"We would have taken away a lot of pain for the industry. It feels like the government has been too late coming to the table on this."
