The incident occurred early last Friday evening at about 6.30pm.
The woman was walking from the beach back to her accommodation up the roadway between Muri Beach Club Hotel and the Rugby Field (Nukupure Park) when attacked.
She told police that two men on a white-gray rental motorbike drove up behind her. One got off the bike and made a grab for the bag from her.
Police spokesman Trevor Pitt said a struggle ensued but the assailant finally overpowered the victim and ran back to the waiting bike rider.
The pair then sped off.
Pitt said: “A good description was provided and they did not appear to be local Cook Islanders, but Caucasians.
“If visitors committed this then there is a good chance they’ve left (the island) already.
“It sounds like a calculated move.”
He said the access road is generally safe “although the time may be important given there are fewer people around – no witnesses”.
“So perhaps it was more opportunistic than anything.”
Police do not have a list of items taken by the robbers.
Pitt asked people to stay alert when in less frequented areas and “be conscious about your belongings – even on the beach”.
Online reaction to the incident was strong with people disgusted by the thieves.
They also voiced concerns about how this may reflect badly on Rarotonga.
In addition, police are investigating two reported burglaries, as well as another case of theft.
The reports of break-ins occurred in Titikaveka and at Arorangi. The latter involved an amount of cash.
Police investigations into the thefts revolve around the taking of keys and a phone from a business property.
There was a rise in burglaries on Rarotonga in June of this year going from 78 for the first six months of the year to 85. In the same period of 2016 57 break-ins were reported.
At the time, Pitt said police had a range of difficulties to deal with in the investigation of burglaries.
“In many cases, offenders break in through doors and windows but manage to do so undetected by any witnesses. The community also remains at risk to repeat offenders as police efforts are continually stretched with monitoring and locating suspects. In many cases (they are) individuals who are already under court orders of curfews and other conditions.
There was a need for improved security around holidays and for neighbours to keep an eye on empty homes or accommodation units.
Both island residents and visitors also needed to take more care of their personal belongings and valuables, Pitt added.