"I spoke to his team this morning and they are very optimistic..they don't think there is anything for us to be alarmed about at the moment. [It's] business as usual and I'll be at the airport [next week].
Budge says Tsonga's withdrawal appears to be a "precautionary measure".
"It's not surprising in exhibitions - it happens quite frequently," added Budge. "I suggest he has probably turned up and done his commitment and is probably free from that now. Players have a very different approach to exhibitions than they do to tour events. At the moment it is just managing the first event of the year, with a grand slam in a couple of weeks."
But, with the memories of last year injury nightmares still fresh, Budge is also taking a philosophical approach to today's news.
"It's something that we can't control," said Budge. "What will be will be. We carry on doing our job and we know we have great fields. Jo is headlining that but we know we have depth throughout. As you saw last year someone can come through qualifying and win the tournament. The depth is there and it will be a great week no matter what."
Tsonga, currently ranked world No10, missed the first part of last year, including the Australian Open with an arm injury.
