Lock Shaw was carried off after just four minutes of England’s 20-16 defeat to Ireland at Twickenham last weekend, while full-back Armitage suffered rib cartilage damage.
Both underwent treatment at the Pennyhill Park training camp this week, but team manager Johnson fears he may have to do without both for the Six Nations clash.
“Delon’s rib injury is difficult to call when he will be fit but he and Simon are progressing very well,” he said. “We will know more next week but it is likely, particularly Simon, that they will be ruled out.
“We would like black and white decisions about injuries but they are never black and white. Guys heal at different rates, particularly with ribs. It can be weeks, months or days.”
If Shaw misses out, as expected, then Johnson is expected to turn to Leicester’s Louis Deacon, who has been called up to train with the squad this week, while there could also be a place on the bench for Northampton’s Courtney Lawes.
Lawes’ Saints’ team-mate Ben Foden, is also in line for a first Test start should Armitage fail to recover.
Johnson will be hoping his England side can rediscover the winning formula when they face the winless Scots next weekend, but admits that lessons need to be learned after Tommy Bowe’s late try earned the Irish a dramatic late victory last Saturday.
“We had a very uncomfortable debrief because we only have ourselves to blame,” Johnson added. “With six minutes to go we were ahead and there was no reason we shouldn't have won the game. You have got to relentlessly do the job and do it right for 80 minutes.”