Whilst formal identification is yet to take place, the woman is believed to be Leah Palushi who was reported missing from her Gainsborough home on Thursday, October 22.
Police say the 40-year-old man is local to the area.
A Home Office post mortem will take place today as part of the investigation into her death.
The woods are known as Dog Island Wood and still remain secured by police officers.
Senior investigating officer, DCI Hayley Williams, said: “If you walked in or around the woods since Tuesday lunchtime until yesterday morning please give the enquiry team a ring.
“I’d like to speak to any dog walkers, bird watchers, runners or anyone who was in the area, it’s quite important.”
“One man has been arrested by the enquiry team, he is local to the area.”
Local community policing inspector, Simon Outen, said: “It’s very sad that a young woman and mum has lost her life. Local officers are out on patrol, please speak to them if you have any concerns.”
Anyone who has information or can help with enquiries is asked to contact Lincolnshire Police on the non-emergency number 101. Alternatively they can call Crimestoppers anonymously on 0800 555111.