Sturridge recently sustained a thigh injury, while Wilshere was substituted in the first half of Arsenal's 1-0 win over Tottenham Hotspur on Sunday due to stomach cramps. Both players are nonetheless expected to remain with the squad for Friday's FIFA World Cup™ qualifier at home to Moldova and the trip to Ukraine four days later.
Winger Theo Walcott played down the significance of the duo's absence from training. "He (Sturridge) is here - that is the positive," Walcott said. "Hopefully Dan can get over the knock. He played with it (against Manchester United on Sunday), I think, so fingers crossed he will be OK for Friday and Tuesday."
On his Arsenal team-mate Wilshere, Walcott added: "He's had an illness so he needs an extra couple of days to recover. I am sure he will be fine, hopefully."
Cardiff City centre-back Steven Caulker and Spurs striker Jermain Defoe were also absent from the morning session at St George's Park in central England, but they were due to take part in light fitness exercises later in the day.
England manager Roy Hodgson has already seen three players withdraw from his squad.
Liverpool right-back Glen Johnson and Manchester United defender Phil Jones both picked up injuries during their clubs' Premier League clash on Sunday, while United striker Wayne Rooney was ruled out with a head injury.
He can call upon Everton teenager Ross Barkley and Spurs winger Andros Townsend, however, who trained with the squad for the first time on Monday after being handed their first senior international call-ups.
"It's a great opportunity for youngsters coming into the squad, that they are going to take their chance," Walcott said.
"I came in at such a young age and I got a hat-trick against Croatia (in a 2010 FIFA World Cup qualifier in September 2008). Anyone can do that against Moldova and Ukraine. There are chances there to be taken. It's only going to be positive when you see these youngsters coming through.
"It is important to get to know the players and staff and the set-up here. It helps you when you go to tournaments. It helped me when I went to the 2006 World Cup. I didn't feature but I knew what to expect at the next tournament, which sadly didn't happen. You want to see the best young talents come through very early and they will only improve."
England currently trail Montenegro by two points in European qualifying Group H, but have a game in hand.
"We are very professional, we know the task ahead and we have to treat Moldova with respect. Ukraine is the big one," Walcott said. "I like to look at games coming up. Hopefully we can have a good performance and not pick up any injuries going into Tuesday's match."