Giggs was pictured on the front pages of national newspapers after he was identified by a member of parliament as the footballer who had gained a High Court injunction preventing allegations of an affair being published.
The 37-year-old Welshman was not the only player missing from training as the English title winners prepared for Saturday's Champions League Final against Barcelona at Wembley.
Defender Rafael, midfielder Paul Scholes, goalkeeper Edwin van der Sar and striker Dimitar Berbatov also sat out a session watched by around 200 reporters.
Giggs, one of United's most influential players this season as the club sealed a record 19th English title, is expected to be in the starting line-up for Saturday's showdown against the Spanish champions.
In a news conference after the training session, United manager Sir Alex Ferguson deflected questions about Giggs.
"All the players are important, every one of them," Ferguson snapped when one reporter asked how big an influence Giggs was on the team.
Police said a group of men vandalised cars belonging to reporters which were parked outside Giggs's home on Tuesday.
"Officers attended and discovered at least six cars had been vandalised after a group of offenders arrived in a Ford Transit van and attacked the vehicles," Greater Manchester police said in a statement.
Media, citing reporters at the scene, said tyres were slashed, and cars pelted with flour and eggs.
