Yorkshire Sculpture Park said 100,000 people visited in September when the poppies were installed, compared with about 37,000 last year.
The poppy arch segment, Wave, consists of 5,800 ceramic poppies falling from Cascade Bridge into the Lower Lake.
Park entry on Remembrance Sunday and Armistice Day will be by ticket only.
Yorkshire Sculpture Park said visitor numbers would be restricted on 8 and 11 November "to ensure a calm and contemplative experience for all".
Belinda Eldridge, operations manager, said the 170% rise in visitor numbers was "phenomenal" and Yorkshire Sculpture Park was expecting its biggest ever year, with more than half a million visitors.
"We feel extremely privileged to be able to bring the poppies to Yorkshire," she said.
"It's safe to say tens of thousands of people are coming as a result of the poppies."
She said the sculpture had a "different feel" from any other sculpture at the park, and many people found seeing the poppies was a "calm and contemplative experience".
The installation is part of a nationwide tour of poppies from the artwork Blood Swept Lands and Seas of Red, which was unveiled in London in July 2014.
The artwork, created by artist Paul Cummins and designer Tom Piper, marked 100 years since the start of World War One and drew more than five million visitors.
The Yorkshire Regiment raised 24 Battalions served by 65,000 men, of whom 9,000 died.

In 2008, elderly residents were moved out of Greyhound Opening in Norwich and senior city council officers moved in.
The council's head of neighbourhood and strategic housing, Kristine Reeves, was later sacked over the affair.
The development proposals, put forward by Norwich City Council, include 60 flats and 45 houses.
The report to the council says 35 of the houses and flats will be for social rent.
A report to Norwich City Council's planning committee, which meets on Thursday, advises councillors to approve the plans.
Elderly residents were moved out of Greyhound Opening and nearby Goldsmith Street seven years ago after Norwich City Council agreed to redevelop the site.
The council agreed that new employees relocating to the city could move in temporarily ahead of demolition.
However other staff, including Ms Reeves, also moved in, in contravention of council policy.
The council resisted calls for a full independent inquiry.
Its own investigation found safeguards covering conflicts of interest were in place but not followed.
In February 2009, London-based architects Riches Hawley Mikhail won a competition to design a new social housing development on the site, but they were never commissioned.
During that year homes on the derelict site were demolished, but the site has since remained untouched.

The move comes after Mexico drew their opening Confederations Cup game 2-2 with Portugal in Russia.
Fifa has since warned the FMF about "insulting and discriminatory chants" and said it could take further action if it happens again.
Mexico have already been fined eight times during World Cup qualifying because of homophobic chanting.
Some fans of Mexico shout an insult at keepers when they take a goal-kick which is argued to be homophobic.
"As you know, Fifa is very serious about the chanting that we do when the goalkeeper takes a kick, and the possible sanctions are serious," said a statement from the FMF.
"Our efforts on the pitch will come to nothing if, because of this (behaviour), we lose the match, the game is suspended or you are expelled from the stadium.
"We lose, you lose, everyone loses."

Aiton, 30, had scans to diagnose the injury on Monday.
He joined the Dragons from Leeds at the end of 2015, and missed the end of the last campaign with an arm injury.
The Papua New Guinea player played 94 games for both Wakefield and Leeds following his move from Cronulla-Sutherland Sharks in 2012.
A sculpture park near Wakefield has reported a 170% rise in visitors since poppies from the Tower of London went on show in September.
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Plans to build 105 homes on the site of a housing scheme in Norwich - which was at the centre of a "homes for staff" scandal - have been put forward.
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Mexico's football federation (FMF) has asked a "small group" of its fans to stop a chant Fifa says is homophobic.
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Catalans Dragons will be without hooker Paul Aiton for up to six weeks after he tore a pectoral muscle on his debut, in a defeat by Wigan Warriors on Friday.