The shark had been spotted further out at sea by paddle-boarder Dana Richardson, where it had also trailed him, but stopped when he got over a sandbar. He headed for shore to alert lifeguards, but the shark had already got there.
"I didn't want to just yell, 'shark, shark,' and scare people," said Richardson. "But when I saw the fin following the kayaker, I began yelling and waving my paddle."
Szulc said he was about 50 metres from shore when he saw Richardson hold up his paddle and point it at him.
"I figured he was trying to tell me something," Szulc said. "I looked back and saw the fin and the body of the shark right behind me."
Debbie Dutton, who was on the beach, said: "It was longer than the kayak. It was crazy big."
The famous John Williams Jaws soundtrack did not kick in at this point, and Szulc managed to outpace his stalker to the shore.
Nauset Beach, among the most popular beaches on the lower portion of Cape Cod, was closed briefly on Saturday after Szulc's encounter with the shark.
Wildlife officials said an increased population of seals in the Cape Cod area was probably the reason for the increased shark activity. There have been at least 15 shark sitings in the region since September 2009.
Jaws, the 1975 Steven Spielberg film about a small New England community terrorised by a great white shark, won three Oscars but also contributed to a huge fear of sharks in the United States.
