Southampton midfielder Adam Lallana has also been named in the 28-man party along with Saints striker Rickie Lambert.
Rodriguez, 24, has made only one appearance for the England U21 side back in 2011 but has been rewarded for his fine form this season, with three goals in 10 matches during Southampton's flying start to their Premier League campaign.
Lallana, 25, is also uncapped but was drafted into the senior squad for last year's game against Ukraine.
Hodgson said: "Adam was with us once a long time ago but he came in late and didn't play so we did see him in training.
"But of course we have been following him very closely and I think he has played a major part in Southampton's rise to the top this season. They are playing very well and he is an important cog, so I think it was quite obvious we would pick him.
"When it comes to Jay Rodriguez, Danny Welbeck at the moment has been injured. We hope and believe he will be fit to play - but I see Rodriguez as someone who could possibly fill that Welbeck role.
"He is a wide forward rather than a midfielder or a winger. He likes to go forward, attack people with and without the ball and get into the penalty box.
"We think he has played well for Southampton and we think this might be an interesting opportunity for us in nine days of training and a couple of games to get to know a little bit more about him as a staff, because up to now our information about him has been gleaned from the stands, not from actually working with him."
Liverpool midfielder Jordan Henderson has earned a recall to the squad but there is no place for youngsters Saido Berahino, Ravel Morrison and Luke Shaw who had all been tipped for promotion from the U21 squad.
Midfielder Jack Wilshere has been included despite fears over his ankle injury while his Arsenal team-mate Kieran Gibbs also gets a recall as additional cover at left-back.
Celtic goalkeeper Fraser Forster is included in the squad as expected and he will challenge Joe Hart for the No 1 spot - although Hodgson has confirmed the Manchester City keeper remains his first choice.
Hodgson said: "Joe will start one of the two games, but I don't think he will start both because I feel it's important for me to look at one of the other two keepers, possibly both, I haven't decided yet. But Joe is still our No 1 goalkeeper.
"I would guess it's more likely he will start against Germany rather than Chile but I don't wish to be held to that."
England play Chile at Wembley on Friday November 15 with Germany arriving at the same venue four days later.
Hodgson has only one more squad to select after these games - for the friendly against Denmark at Wembley in March - before naming his provisional 30-man party for the World Cup finals in Brazil next summer.
Squad: Forster, Hart, Ruddy, Baines, Cahill, Cole, Gibbs, Jagielka, Johnson, Jones, Smalling, Walker, Barkley, Carrick, Cleverley, Gerrard, Henderson, Lallana, Lampard, Milner, Townsend, Wilshere, Defoe, Lambert, Rodriguez, Rooney, Sturridge, Welbeck.