The device could be worn over natural hair and would process data, communicate with other devices, navigate roads and collect medical information.
The company hopes its invention will lead the way for the ever growing wearable technology sector.
Andrew Milroy, an analyst with consulting firm Frost & Sullivan, told the BBC: "Wearable gadgets are definitely going to be one of the big areas of growth over the next two years."
He added: "And Sony - which is trying to regain some of the sheen it has lost in recent years - clearly understands that and wants to play a major role in the sector."
Sony said in its application the wig could be made from horse hair, human hair, wool, feathers, yak hair, buffalo hair, or any synthetic material.
The sensors would be almost completely hidden by the hair to make it look more natural and increase user comfort.
And the firm hopes the wig would help blind people navigate roads, with a small camera or sensor recording the user's position.
A remote user would then use the images provided and send vibration commands through the network to direct the user manually.
Sony said in its application: "Although navigation systems based on vibration motors have been widely introduced, a navigation system integrated into a wig... is so far not known."
Sensors would also help collect information such as temperature, pulse and blood pressure of the wearer.
And it may be used during presentations, with the user being able to "move to the next presentation slide or back to the preceding presentation slide by simply raising his/her eyebrows."
Sony told the BBC it hasn't made any plans for commercial production of the SmartWig yet.