The team, founded by five-time Olympic champion Sir Bradley Wiggins to develop young British talent, was omitted from the race which runs from 28-30 April.
"It's very disappointing and it is very much a surprise," said the team's sports director Simon Cope.
Race organisers said the event was oversubscribed and "unfortunately someone had to miss out".
A total of 49 teams applied for 36 slots - 18 in the men's race and 18 in the women's.
The decision on who was included was made between Welcome to Yorkshire and cycling event organisers ASO, who jointly run the event.
A Welcome to Yorkshire spokesman said that Team Wiggins were welcome to apply for any future editions of the race.
But Cope told Cycling Weekly that he believed the team, who are the only British third-tier UCI Continental outfit not included, could have made an impact in the race.
"Good or bad press at the moment, there's a percentage of the UK population who will be going to the race who want to see (Team) Wiggins there," he said.
"You would have thought that we would have got in, but the organisers have made their selection and that's it, we can't do anything about it. We will have to go and find another bike race to do."
An investigation by UK Anti-Doping is currently ongoing into allegations of wrongdoing in cycling involving Wiggins - who retired in December - and Team Sky.
Cope, who used to work for Team Sky, was questioned by MPs earlier this month about the contents of a medical package he delivered to Wiggins when he was racing at the 2011 Criterium du Dauphine in France.
Team Sky have admitted "mistakes were made" around how medical records relating to the package were kept but deny breaking anti-doping rules.

The FAI accepted 5m euros (Â£3.6m) from Fifa in 2010, in return for dropping court proceedings over Thierry Henry's handball in a 2009 World Cup play-off.
The FAI described it as an "interest-free loan" that was accounted for in its 2010 audited financial statements.
It said the 5m euros was recorded under "bank and other loans" in its accounts.
The timeline has been published on the FAI's website, and includes copies of its written agreement with Fifa and relevant bank documents.
It confirms that in 2013, the remaining loan amount was "reduced to nil as a result of the non-qualification for the World Cup South Africa in 2010 and the World Cup Brazil in 2014".
Details of the timeline were released just hours after Irish prime minister Enda Kenny publicly urged the FAI's chief executive John Delaney to explain the Fifa deal.
Mr Kenny described the payment as "quite extraordinary" and said the FAI boss must answer questions "in the interests of transparency and accountability".
The Republic of Ireland team was 16 minutes away from a penalty shootout for a place in the 2010 finals in South Africa when Henry handled in the build-up to William Gallas's extra-time equaliser in the second leg of the play-off in Paris.
In its latest statement, the FAI said that because FIFA has confirmed the transaction, FAI Board members believed they were "no longer obliged to abide by the confidentiality agreement" struck as part of the deal.
Its timeline detailed how the FAI wrote to Fifa in November 2009, saying it was considering referring the handball dispute to the Court of Arbitration for Sport.
In a press conference later that month, Fifa president Sepp Blatter joked about the FAI's request to be the 33rd team at the World Cup, which the FAI claimed caused it "reputational damage".   Mr Blatter later made a personal apology for the remark.
Following negotiations with Fifa in Zurich in January 2010, the FAI said FIFA offered it  "a 5m euros interest-free loan by way of compensation as well as a 400,000 euros (Â£290,000) Goal Project grant that was used for FAI Regional Football Centres".
It added that the 5m euros was lodged in to FAI's National Irish Bank deposit account on 20 January, 2010.
"This funding was used to make payments to New Stadium Ltd (trading name for Aviva Stadium management company) on February 25 and March 26 of 2010," the FAI statement said.
It said it had released the details "to demonstrate that the Board of the Association acted at all times in the best interests of Irish football, and in full compliance with Irish company law".
Team Wiggins say they are "surprised" and "disappointed" after being excluded from next month's Tour de Yorkshire.
[NEXT_CONCEPT]
The Football Association of Ireland (FAI) has released the timeline of its controversial multi-million-euro deal with Fifa to stop a legal battle.