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, 32, has vowed he will play for England as long as he is wanted.
With a round of international fixtures sandwiched in between two weekends of domestic football, there have been a raft of withdrawals from the squads of all the home nations, prompting talk that club now takes precedence over country.
But Lampard 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.
