The 29-year-old Saracens flanker dislocated the fibula head just below his left knee when playing against Treviso in the Heineken Cup in January and had to watch as Scotland lost every match in the Championship to pick up the Wooden Spoon.
He intended to return in time for the Premiership champions' end-of-season run in and hoped to win back his place in the national team for June's matches against Australia, Fiji and Samoa.
Brown has not played for Scotland since World Cup and admits the latest news left him massively frustrated but promised to spend his enforced lay-off in a positive manner.
"I phoned and spoke with Andy (Robinson) last week and said it's going to be too soon," Brown told the Scotsman.
"It's a shame because I'm desperate to get back - I absolutely love playing for Scotland and it feels like I have not done that for a really long time.
"Having said that, I am using the time off well. I'm working hard and I'm determined to come back even stronger and fitter.
"I'm not going to put a date on it but I would hope to be back by the start of next season."