A number of areas in Twyford Woods were targeted between Sunday and Monday, including a wall and a disused fuel drum.
During the Second World War, the site was used as an airfield for aircraft to take off for Normandy ahead of D-Day.
Last week, the Queen paid tribute to the "heroism" of troops, marking 75 years since the Normandy landings that changed the course of the conflict.
Special events took place throughout the day to mark the historic military offensive, including a flypast by the Red Arrows in Portsmouth.
Following the attacks in Lincolnshire, police urged anyone with information to come forward.
In a statement, the force said: "Between Sunday 9 June and Monday 10 June, a number of areas within the Twyford Woods site have been defaced with swastikas in silver and white spray paint.
"This includes a commemorative bench which has been extensively vandalised.
"We are appealing for witnesses to this vandalism and anyone with any information that can assist with our investigation to contact us."