Blues midfielder Lampard has been given the armband after regular captain Rio Ferdinand was ruled out with a groin injury suffered ahead of Manchester United's game with Wolves on Saturday.
Steven Gerrard would have been favourite to replace Ferdinand but will also miss the game due to injury despite playing 90 minutes of Liverpool's win over Chelsea on Sunday.
Lampard has suffered major injury woes this season, and has not been involved with England since August, but England boss Fabio Capello believes he will be one of the fittest players on the pitch at the 38,065-capacity Parken Stadium on Wednesday night (kick-off 7.15pm GMT).
"I spoke with him about injuries that he suffered and I have been monitoring him during the last give games that he played," Capello said.
"He improved a lot. I saw the game they played against Liverpool and he played a really good game. I followed him practically the whole game and I think at this moment he is probably fresher than the other players."
Lampard will line up alongside Wilshere in midfield, with the Arsenal youngster being asked to play a more defensive role than he has in the past.
But Capello is confident the 19-year-old is ready.
"In the last two months he has improved a lot with his confidence and also the confidence of the other players like Cesc Fabregas and (Andriy) Arshavin when he has the ball," Capello said.
Capello also confirmed that Aston Villa's record signing Darren Bent will start the game.
"I have watched two games he has played for Aston Villa," Capello said. "When he was with Sunderland he played a different style because the manager asked him to stay close to the box and be fresh to score goals, but now he runs a lot more, presses a lot because the team play with a different style.
"He played well before but if you want to play with the seniors at this moment you have to be good when you go forward but also when you have to win the ball back and I think he has improved a lot."
Capello also insisted that he had no doubts over the motivation of his team to represent their country, despite fresh questions being raised by another rash of high-profile withdrawals from international duty.
"I never saw this," Capello said. "All the players that played with England, they try to do the best for us in every moment.
"I think this team have found every time a good spirit and I am really happy with these players and the players that played before.
"Sometimes people don't see or can't understand that they played with pride, but the performance every time is 100%. Sometimes 100% is not enough (to win)."
Lampard, meanwhile, has vowed he will play for England as long as he is wanted.
The 32-year-old said: "Until the day they don't want me I will always be available for England. I will always have the appetite to contribute and do well.
"It's a short career and it's an honour to represent your country. I will always try and be there.
"If you're fit and you come here, you want to play 90 minutes against Denmark and that's the way it should always be.
"It will always be a huge honour to play for your country.
"I know from mixing in the squad how important it is to everyone.
"After the World Cup, it's very easy to say the players didn't care. Of course the players care. We just didn't win."
With regular captains Rio Ferdinand and Steven Gerrard sidelined through injury, Lampard will lead the players out for the first time in an England shirt.
"I'm very proud," he said. "I've been in the squad quite a long time and I feel like one of the older stagers.
"It will be one of the proudest moments of my career.
"To actually walk out (as captain) is a huge deal. I've been in awe of many a player who's done that. You grow up dreaming of that moment."
Lampard is looking forward to playing alongside Wilshere in midfield - and expects the impressive Arsenal youngster to shine in what will be his first start.
"I don't think he needs much help, the way he's playing," Lampard added.
"He's been fantastic for Arsenal. Some players take a while in the transition into the full team. He looks like he's got the mental attitude to fit right in.
"I'm looking forward to playing alongside him."
Lampard also praised club-mate Ashley Cole, often the target of boos from the England fans but recently voted the supporters' player of the year.
"He's quite well recognised now as our greatest ever left-back," Lampard added. "It's great to see the England fans, once they take away some of the nonsense from outside and talk about his performances, to see him get recognised as the best player of the year."