Ziyech was forced off with a hamstring problem during Chelsea’s 3-1 win over Leeds United in the Premier League last Saturday.
Meanwhile, Hudson-Odoi also suffered a similar injury in training ahead of Chelsea’s 1-1 draw with Krasnodar in the Champions League on Tuesday evening.
A two week lay-off means that Ziyech and Hudson-Odoi are likely to miss Chelsea’s Premier League fixtures against Everton, Wolves and West Ham.
But the pair could return for Chelsea’s trip to Arsenal on Boxing Day.
‘Both players are hopefully going to be missing for around two weeks,’ Lampard said after Chelsea’s draw with Krasnodar.
‘They had scans yesterday and they’re showing it will be about two weeks so I think that’s positive, particularly with Hakim.
‘With Callum, we didn’t know what to expect because it was an injury he got in training a couple of days ago.’