The 30-year-old sustained the injury in the 22-9 PRO14 victory over the Dragons and he will now require scans to learn the full extent of the damage.
Ospreys expect that Lydiate will miss their European Champions Cup pool matches with Saracens and Clermont later this month, while they fear he could be sidelined for up to 16 weeks.
Ospreys defence coach Brad Davis said: "I know players before who have had bicep tears and have had operations and been out for 12 to 16 weeks, possibly longer.
"It really depends on the extent of the injury. The best-case scenario is six to eight weeks. The worst case is they have to operate.
"We'll know a lot more about that once he has a scan and the medics can plan the way forward."
Wales kick off their Six Nations campaign on February 3 against Scotland and Lydiate could face a race against time to recover for the clash.