Australia are fresh from a successful 2-0 tour of the West Indies but Michael Clarke's men have no further Tests until their home series against South Africa in November.
Ponting was dumped from Australia's one-day international squad in February, meaning he will not be playing much cricket in the lead-up to South Africa.
But Arthur moved to quash speculation that the 37-year-old champion run-maker could be leaving the team.
"I know there was a lot of media pressure and talk around Ricky, but Ricky's not going anywhere," Arthur said on his return from the West Indies.
"We hope Ricky's scoring enough runs to go to the Ashes in England.
"Ricky is definitely no way considering retiring, I wouldn't have thought from my conversations with him, and he'll be fit and ready to go against South Africa."
Ponting has played 165 Tests over 17 years and is Australia's all-time top run-maker, but his position has come under scrutiny.
Despite tough conditions in the West Indies, he helped put Australia in a commanding position in the third and final Test but his highest score on the tour was just 57.
That innings ended in bizarre fashion when he ducked under a Kemar Roach bouncer but left his bat sticking up like a periscope, only for the ball to hit it and fling a catch to Shivnarine Chanderpaul.
"I feel sorry for the bloke because he has been batting beautifully and again it will give ammunition to some bloody journalist back home," his partner at the crease Ed Cowan said after the match.
Arthur said difficult conditions and unlucky circumstances affected Ponting's run total of 146 over the three Tests in the West Indies at an average of 24.33.