Of the total foreign entrants, about 80% would not be required to furnish proof of negative Covid-19 tests, nor would they have to quarantine on arrival. This includes people from all other members of the G7 group of developed economies.
Japan is accepting business travellers, foreign students and academics but not tourists, except for a limited number in a trial of package tours.
Matsuno said experience with the trials would be used in later decisions to further reopen.
Japan had earlier this week also announced that it will begin allowing small package tours from four countries before gradually opening up to foreign tourism for the first time since it imposed tight border restrictions due to Covid.
Transport minister Tetsuo Saito said the tours will be allowed from Australia, Singapore, Thailand and the United States as an experiment.
Participants must be triple-vaccinated and the tours must have guides and fixed itineraries, the Japan Tourism Agency said. Each tour can have a maximum of four people, and a total of 50 participants are expected to join the experiment.
The participants will enter Japan on a special visa, not a tourist visa. The results will be used to compile coronavirus guidelines for tour operators, hotels and other related businesses.
The experiment is expected to start sometime next week and continue until the end of May.
Japan's tourism industry, hit hard by the strict border controls, is eager for foreign tourism to resume. Covid-19 infections have slowed in Japan since earlier this year and the government is gradually expanding social and economic activity, including easing restrictions for travel.
Prime Minister Fumio Kishida said in a speech during a visit to London earlier this month that he plans to ease the border controls as early as June in line with the policies of other Group of Seven industrialized countries, but gave no further details.