Barry was granted compassionate leave after his brother, Marc, died aged 39.
The former Manchester City player featured for the 'Baggies' in a behind-closed-doors friendly against Brentford on Tuesday, but it has been made clear he can have more time off should he need it.
"This is terrible news for Gareth and his family and everyone at the club extends their condolences," manager Darren Moore told the club's official website.
"Gareth knows that he can rely on our full support and understanding in helping him cope with this tragic event."