Rafaella and Massa have been married since 2007 and are expecting their first son.
Massa qualified in 10th despite the crash but will miss Sunday's race and Ferrari will not be able to nominate a replacement driver, as he would have to have driven in the qualifying session.
The accident bears similarities to one last weekend at Britain's Brands Hatch circuit when Henry Surtees, the son of former F1 world champion John Surtees, was killed during a race after being struck by a wheel.
The freak accident occurred when driver Jack Clarke's car hit a tyre wall and a wheel came off, hitting Surtees on the head.
Barrichello, who visited Massa at the circuit's medical centre, said he thought both accidents were a clear sign that there was a need for improved safety in motorsport.
'It is not a coincidence something happened right now. In the GPDA (Grand Prix Drivers Association) we talked quite a lot about it yesterday - and something needs to be done,' said the Brazilian.