The Brawn driver told reporters that doctors would not let him see Massa, 28, when he visited the AEK hospital on Saturday, and that they "weren't able to tell me if he will be okay".
"It is a bit of an emotional moment," said Barrichello, who admitted he is torn between wanting to stay in Hungary and returning home to his wife and children.
"It is burning a little bit in my stomach, and I would be lying if I said I wasn't thinking of him in the middle of the race," he added.
FIA medical delegate and F1's travelling doctor Gary Hartstein, meanwhile, told Italy's La Gazzetta dello Sport when asked about Massa that "weeks, if not months, must go by before we know for sure how he is recovering".
Police escorted the Ferrari driver's family, including his parents, brother and pregnant wife Rafaela, to the central Budapest military hospital on Sunday morning, and have remained at his bedside constantly.
Massa's personal doctor Dino Altmann was also with the entourage, and Ferrari president Luca di Montezemolo is due to arrive in Hungary on Monday.