The Spaniard told his followers on Twitter that it had been a "great day" at the Woking factory while McLaren said the double world champion had focused on operational work and practising qualifying and race procedures.
Alonso missed last weekend's season-opening Australian Grand Prix, his first race back with McLaren after leaving Ferrari, on doctors' orders after crashing and suffering concussion in Barcelona at the end of February.
He must still satisfy the governing International Automobile Federation that he is fit to race but expects to be driving again at Sepang and has posted photographs of himself swimming and working out.
McLaren made a dismal start to the season and their new partnership with Honda, Jenson Button and stand-in Kevin Magnussen qualifying on the back row of the grid in Melbourne.
Magnussen did not even make it to the grid on Sunday after his car's engine blew while Button, the last driver to win a race for McLaren back in 2012, finished 11th and last after being lapped twice by world champion Lewis Hamilton.
(Reporting by Alan Baldwin, editing by Ed Osmond)
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