According to reports, the tree fell just after 2 pm, close to the south entrance of Woodford Square.
The two Venezuelan nationals, identified as Jairo Jose Fontt Acosta, 22, and Yullanis Perez, 20, were sitting on a bench when the tree came crashing down on them.
Eyewitnesses came to their rescue and pulled the two from under the tree.
Their injuries were not immediately clear but they were listed as serious.
Fire and police officials responded and rushed the two to the hospital.
One eyewitness, Carol Turner told Guardian Media that they heard the noise and then heard people shouting that two persons were under the tree.
“That is when I ran under to help and remove the women and her personal belongings. Her shoulder was in a lot of pain and (she was) bleeding. The man was removed by other persons,” she said.
Turner lamented, “I pass in the Woodford Square daily and I always watch this tree and I knew that it was rotting but I would have never thought it would have fallen on someone, that is the first time I see something like this.”
The area where the tree fell is now cordoned off from the public.
Investigations are continuing.