Spokesperson Mihlali Majikela said the men demanded their belongings and hit one of the women on the head when she refused.
She fell to the ground, but a resident in the area saw the commotion and called a security company for help.
HALT security’s George Conradie told News24 that one of its guards patrolling the Durbanville area responded to the call.
The guard gave chase and caught one of the men.
“There was a tussle,” said Conradie, adding that guards in another two vehicles raced to the scene to help and tackled the man and held him until the police arrived.
Majikela said the second person suspected of being involved in the attack was caught by Durbanville police.
The two face charges of robbery.
Comment from the women was not immediately available, but Netwerk24 reported that Claire Whitwam, 63, and her daughter, Brigette, 34, had gone for a walk at around 14:30 when they were attacked near Sonstraalhoogte.
Their dog was also hit by the men.
In a post on HALT’s Facebook page, one of the women expressed deep gratitude to the security company for its help.
“We are thrilled that they chased down and caught one of the attackers who is in police custody.”
She said the attackers had hit her on the head and broke her daughter’s hands, adding her daughter was also stabbed in the breast.
Whitwam said a specialist had to see to her daughter, and she needed to see a dentist for several broken teeth, adding she also needed to be treated for a 7cm gash on her head.
“We are all a bit traumatised but will live to fight another day.”
Whitwam said the robbers stole her wedding band, a thin silver chain with a small crucifix on it, and her fitness watch.