Police are appealing for witnesses following two incidents in Norbury last Friday.
They both occurred in Highbury Avenue between 3.20pm and 3.30pm on Friday 23 November.
In the first incident a woman in her 40s was approached by a man in possession of what was described as a machete with wooden handle. The woman ran away immediately.
The man was described as black, 18-20 years old, around 5ft 6ins tall, medium build with short dark curly hair and was apparently wearing dark trousers and a grey round-neck top.
In another incident, a 16-year-old boy was walking along the same road when he was hit on the head from behind. The victim ran off and did not see his attacker. He went to hospital but was later discharged.
Police say they are keeping an open mind as to whether the two are linked.
Detective Inspector Simon Harding, from Croydon CID said: "We're appealing for anyone to come forward who might have seen the male described or who may have seen either of these incidents take place.
“Both incidents are very unusual and seemingly unprovoked and we would urge anyone with information to come forward immediately - particularly if you saw a man acting suspiciously, matching this description in or around the Upper Norwood or Norbury area on Friday afternoon.
He added: "I also want to reassure the local community that we have put in place extra police patrols in the area.
“As I've said, these sorts of unprovoked incidents are very unusual and my officers are carrying out extensive enquiries to try and establish what happened. We would ask the public just to remain vigilant and if you do see anybody acting suspiciously, then call 999."
Anyone who witnessed either incident or with information should contact Croydon CID on 020 3276 2172 or the Met's non-emergency number 101. Alternatively, call Crimestoppers anonymously on 0800 555 111.