The 2014 Olympic bronze medallist and triple World Cup champion, 29, underwent emergency brain surgery after sustaining serious head injuries at Innichen in northern Italy in mid-December.
She was transferred to Stockholm in late December and had been in a coma since.
"Anna is having intensive rehabilitation at the Danderyd hospital after her severe head trauma," the Swedish Ski Federation said in a statement on Thursday.
Her health was improving to the point that "it is now possible to communicate with her and even to obtain short answers".
She could return to her hometown of Sundsvall, eastern Sweden, this summer to continue her recovery.
Ski cross, which made its Olympic debut at Vancouver in 2010, consists of lining up four skiers at the same time on a course made of large bumps and narrow turns.