Stander will also be working against the clock to make a full recovery time to make the showdowns with France on March 10 and Wales on March 16.
Billy Holland has joined up with the Ireland squad at Carton House this week ahead of Saturday's Murrayfield clash with Scotland.
"Keith Earls suffered a hip pointer injury and will be managed across the early part of the week".More news: Steve Smith could miss World Cup as ball-tampering ban faces delay
If he is ruled out for four weeks, that would see him missing Six Nations matches against both Scotland and Italy this month.
According to a report in The42, Holland has been called up into the squad by head coach Joe Schmidt this week.
Andrew Conway was injured in training last week, and will undergo rehabilitation with his province Munster.More news: Man accused of kidnapping Jayme Closs to appear in court Wednesday
Stander's brother-in-law, Ryk Neethling, tweeted on Saturday night "proud of CJ Stander playing 62mins with two fractures in his cheek and eye socket".
Ireland approached this year's Six Nations appearing in a position of strength at lock, but were struck by injuries to Iain Henderson and Tadhg Beirne before the tournament even kicked off.
Connacht's Quinn Roux looks set to slot into Ireland's second row alongside James Ryan then, with Ultan Dillane poised to take a seat on the bench. Ringrose's absence means Robbie Henshaw could move back into the centre, with Rob Kearney perhaps brought back in.More news: Nantes demand Sala transfer fee from Cardiff