Doctors have said they will not be able to say before the end of the week if he will live or die.
Johan was trapped under the snow for 15 minutes on Friday while ski-ing off piste in the resort of Lech – where the Dutch royals traditionally take their winter break.
The 43-year-old, who was visited in hospital on Sunday by his mother Queen Beatrix and wife Princess Mabel – has been unconscious ever since he was airlifted to safety.
Officials said Johan – pictured with Mabel and their daughters Luana, seven, and Zaria, six – is stable, but in a critical condition.
Prince Johan's skiing companion has been questioned over the avalanche, say prosecutors.
The 42-year-old friend, who Dutch media have identified as the director of the hotel where the royals are staying, has been questioned by police.
A routine investigation has been opened, and may last several weeks.
Johan's companion, who is also a childhood friend, escaped injury thanks to an avalanche airbag – which inflates to keep skiers at the top of the snowfall.