Police were alerted to the incident about 2.45am and rushed to the scene at Gate 1 of the park on Witthayu Road.
Taxi driver Narasak Poolma, 30, sustained a graze on his forehead caused by a bullet.
The left side of his taxi was riddled with bullet holes, windows had been smashed and a front tyre and a rear tyre punctured. Many spent bullet cases were scattered nearby.
A passenger who travelled in the taxi fled the scene, police said.
Mr Narasak told police that he drove a drunken passenger from Rama II Road to Lumpini Park.
When the taxi stopped at the park, they heard a man, who they believed to be a PDRC security guard, shouting from inside the park, telling them to move away.
Then, the sound of a giant firecracker was heard before sounds of gunshot followed, Mr Narasak told police.
PRDC spokesman Akanat Promphan later held a press conference denying speculation that the taxi was attacked by protest guards.
According to him, witnesses said they spotted a taxi driving round the park before someone in the cab opened fire into the park from Gate 2 to Gate 1, prompting a return of gunfire.
Mr Akanat said that the PDRC did not know who returned fire.
Meanwhile, protesters led by the Network of Students and People for the Reform of Thailand (NSPRT), an ally of the PDRC, yesterday turned up at Dusit police station.
They demanded an explanation for the arrest of a security guard who was detained for possessing a tear gas mask.
The security guard, arrested on Saturday night by Din Daeng police, was charged with illegal possession of military hardware or war material.
NSPRT chief guard Nasser Yeehma insisted that tear gas masks can be used to protect the wearer from chemicals in industrial plants and are available at homewares stores.
The Civil Court has also banned police from seizing protesters' equipment, Mr Nasser said.
Dusit police chief Pol Col Supakit Torboon met with the protesters and admitted that it was the police's fault and a misunderstanding led to the arrest of the security guard.
In another development, a network of doctors and medical and public health personnel yesterday issued a statement condemning the M79 grenade attack on Mongkutwattana Hospital on Chaeng Watthana Road on Friday night. No one was injured.
The network includes deans of medical sciences faculties from nine universities, dentistry faculties from six universities, deans of 13 pharmaceutical sciences faculties and 24 public health associations nationwide.
The network said the attack has intimidated patients and medical personnel who offer treatment to people regardless of their political ideologies.
Permanent-secretary for public health Narong Sahamethaphat, along with personnel from the medical network, yesterday presented flowers as a gesture of moral support to Maj Gen Rianthong Nanna, director of the Mongkutwatthana Hospital, after the incident.