Walton suffered the stroke several weeks ago, just a few weeks after taking over as general manager of Mavic's U.S. operations.
The former pro cyclist is "doing really well," his wife Susan said in an email to BRAIN.
"For the past few days he has been able to walk short distances unassisted so the physical therapy is going well (no surprise there!). The cognitive and speech therapies are making inroads but take longer for results," she said.
"The rehab hospital is recommending another three weeks of in-patient therapy and then Hugh will start less-intensive outpatient treatment. I'm exploring the possibility of getting him transferred to a facility here in Colorado to be closer to our family."
Susan Walton said doctors have not estimated when Walton will be able to return to work, but are assessing his progress a week at a time.
Mavic spokesman Zack Vestal said the company is committed to supporting Walton's recovery.
"The company is giving him and his family both space and support in this effort," Vestal said.
He said there are no plans to appoint an interim general manager while Walton recovers.
"Before Hugh came on board, the day-to-day responsibilities were handled by a 'trifecta' of department heads: marketing director Sean Sullivan, national sales manager Larry Burke, and accounting supervisor Ron Gioia. From what I understand, they've picked up the additional tasks as they did before Hugh's hire," added Vestal, who works from Colorado.