The 18-year-old midfielder was the only uncapped outfield member of Low's 27-man squad, which will be reduced to 23 men by May 29, while 19-year-old ter Stegen is one of four goalkeepers, one of whom will remain in Germany this summer.
Draxler, who would also be eligible to play for Germany's Under-19s this summer, is one of 12 midfielders selected by Low with the likelihood one or two will be trimmed from the final squad, but Low is looking forward to taking a closer look at him over the coming weeks.
"Julian Draxler has a lot of potential, he is very young and very quick in the one-on-one situations, and very intelligent," said Low after announcing his squad in Rastatt on Monday.
"He still does not quite have the consistency, also because he had other things to deal with, such as attending school, and he is still young and could play for the under-19s, but we think he has a great deal of potential for the coming years and we think this nomination could give him a further boost.
"I spoke again with him this morning [Monday] and his coach Huub Stevens and both are very pleased and we feel he has a great deal of potential."
Ter Stegen's form for Gladbach this season has caught the eye and he enters into a three-man battle for two places alongside number one Manuel Neuer in Poland and Ukraine.
"Ter Stegen has played a fantastic season with excellent performances for his young age," said Low.
"He is already very mature and has a good presence and that is why we chose him."
Ter Stegen joins Tim Wiese and Ron Robert Zieler in the 27-man squad, but Low has not yet decided which of the trio will be left at home.
"At the moment, we have no reason to make any final decisions," said the Germany coach.
"We will do that on May 29. All of the keepers who are here have strengths and they have proved it several times so we have no reason to decide completely yet.
"We have got to remember what can happen in preparations - you can get injuries and realise other things, therefore we will decide which squad to take on May 29, before then we will gather our impressions in training."
Of the players who were expected to be in the squad, but have been left out, Bayer Leverkusen captain Simon Rolfes stands out.
Borussia Dortmund midfielder Ilkay Gundogan, who made his national team debut last October, and his team-mate Sven Bender have been given the nod ahead of him.
"Rolfes has always been with us and he is reliable when in top form," explained Low.
"That has not always been the case for him this season while Ilkay Gundogan has played very well particularly in the second half of the season."
Arsenal defender Per Mertesacker is also included, despite missing the last three months injured, while Lazio forward Miroslav Klose is also in the squad ready to prove his fitness after a long injury absence.
"We have spoken with Per and he has put in a lot of effort in getting back to fitness," said Low.
"I spoke to him and his coach Arsene Wenger yesterday [Sunday]. We agreed that he will fly with the squad to Sardinia on Friday.
"Wenger said he is not ready to play yet so he has welcomed us taking him with us for training.
"He has got to get back to competitive levels of fitness and we hope to get him there over the coming weeks.
"We expect Miro to start next weekend (for Lazio), at least that is his agreement with his coach there.
"I hope both of them get into form. At the end of preparations, I will have to judge if they are capable of coping with the strains."
Germany head into a training camp in Sardinia on Friday, albeit without members of Bayern Munich and Borussia Dortmund's squads as they meet in the DFB-Pokal final on Saturday.
Dortmund's players will then link up with the squad for the second phase of their preparations in the south of France from May 18, although Low will have to wait even longer before his Bayern contingent joins the squad after the Champions League final on May 19.
Since they are also then involved in a friendly match with their club against Holland, they will be given a few days of rest before completing Low's squad ahead of a friendly match against Switzerland on May 26, just days before the deadline for Low's final 23-man squad to be submitted to UEFA.
Germany will also play Israel on May 31 before the final 23 players fly out to Germany's base for the competition in Gdansk on June 4.
Germany's first group fixture is against Portugal on June 9 before they face Holland on June 13 and Denmark in their final group game on June 17.
Goalkeepers: Manuel Neuer (Bayern Munich), Tim Wiese (Werder Bremen), Ron Robert Zieler (Hannover), Marc-Andre ter Stegen (Borussia Monchengladbach)
Defenders: Holger Badstuber, Jerome Boateng, Philipp Lahm (all Bayern Munich), Benedikt Howedes (Schalke), Mats Hummels, Marcel Schmelzer (both Borussia Dortmund), Per Mertesacker (Arsenal)
Midfielders: Sven Bender, Mario Gotze, Ilkay Gundogan (all Borussia Dortmund), Lars Bender, Andre Schurrle (both Bayer Leverkusen), Julian Draxler (Schalke), Toni Kroos, Thomas Muller, Bastian Schweinsteiger (all Bayern Munich), Sami Khedira, Mesut Ozil (both Real Madrid), Marco Reus (Borussia Monchengladbach)
Forwards: Lukas Podolski (Cologne), Cacau (Stuttgart), Mario Gomez (Bayern Munich), Miroslav Klose (Lazio)