The McLaren driver says in a video on YouTube "as you can see, I am perfectly fine.
"I would like to be at the test this weekend, but the doctors' recommendation is to rest a few days."
The two-time Formula One champion crashed Sunday at the Barcelona-Catalunya circuit, ruling him out of the third and final test.
Alonso did not say if he plans to race in the season opening Australian Grand Prix on March 15. McLaren chairman Ron Dennis has said he was hopeful the Spaniard would be fit by then.