Chelsea remain in the final Champions League qualification place, five points ahead of fifth-placed Manchester United, and Lampard knows how important it will be to have his France international back fit and firing.
"I'm hoping short-term. He actually got through training but had an awareness of it," the Blues boss told BBC Match of the Day after Kante's absence unhelpfully coincided with speculation linking him to Real Madrid.
"It didn't break down as such. It's something we'll have to look at in the week ahead.
"We know how important he is for us and he's played so many games over the years regularly.
"This year, not so much – which is unfortunate for everybody here. So we'll look after him and hopefully it's not too long."
Kante has missed eight of Chelsea's 22 Premier League matches so far this term, having been hampered by a series of minor issues.
Christian Pulisic was another injury victim in training at Cobham this week, suffering tendon damage.
The United States' attacker being sidelined created the opportunity for Hudson-Odoi to start and score his first Premier League goal.
"Callum did very well. The urgency of his game, being on the edge, making runs and getting at people – so positive," Lampard added.
"Those are the things that he needs to do, keep working on that. We know the talent he's got."