Curnow left the field in discomfort during the Blues' match simulation session at Ikon Park on Saturday and had his right knee assessed by medical staff.
The two-time Coleman Medal winner was then sent for precautionary scans, which came back clear.
Curnow will remain on a modified training program as he builds back to full fitness after undergoing knee and ankle surgeries in the off-season.
The 28-year-old was only scheduled to take part in half of the Blues' session and looked good early, marking well and kicking a goal.
King was sent for scans after injuring his knee at training on Friday, with the Saints always optimistic he had avoided the dreaded anterior cruciate ligament (ACL) tear.
The 24-year-old tore an ACL in his draft year and has more recently battled shoulder injuries.
Teammates Jack Sinclair (hamstring) and Mason Wood (quad) also left the track early.
On Saturday evening, the Saints confirmed King had avoided any structural damage to his knee while Sinclair and Wood didn't suffer "serious damage".
"Our football program is currently on its four day break, so Max, Mason and Jack will rest over the next few days and we'll assess their resumption of training next week," football boss David Misson said.
It is welcome news for the Saints, who are already without Mattaes Phillipou (leg stress fracture) and Dougal Howard (shoulder) for the start of the year, while Rowan Marshall (pelvis) is racing the clock to play.
Carlton have pre-season hit-outs against St Kilda and GWS this month before starting the home-and-away season against Richmond on March 13.
The Saints also have a pre-season match against Port Adelaide, while they face Adelaide away in their season opener on March 16.
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