Lincolnshire Police urged motorists to avoid the area immediately after the crash, which happened just after midday today.
The road was closed for around two-and-a-half hours until around 2.30pm.
The force tweeted: "We have closed the A52 between Swineshead and Bicker Bar due to a serious RTC
"Please avoid the area and we will update when we have further details. Incident 159 of today."
In an update later, police said: "The A52 at Swineshead remains closed while our investigations continue into an RTC that happened at 12.20 today.
"A red Triumph motorbike is involved and a woman has been taken to hospital with serious injuries, her family are aware."
Shortly afterwards, the force posted that the road had been re-opened.
"We are appealing for witnesses to this collision," a spokesperson for Lincolnshire Police said.
"If you saw the incident or have dashcam footage of the collision or the red Triumph motorbike travelling towards Swineshead roundabout, please call 101 quoting incident 159 of 19/4."