Longtime Lakers trainer Gary Vitti evaluated Bryant on Monday morning and said Bryant's condition is improving, explaining that the grinding or "crepitus" in Bryant's shin has subsided, but that the 16-year veteran still needs more rest.
Bryant wore a walking boot following shootaround Monday and chatted with teammate Ramon Sessions on the bench, but declined to speak to reporters.
Devin Ebanks started in place of Bryant and tallied six points and two rebounds over 26 minutes.
Bryant suffered the injury on March 31 when he was kicked in the shin during the first quarter of the Lakers' 88-85 win over the Hornets.
Bryant was able to play four games with the injury, wearing a protective boot on off days and sitting out of shootarounds to avoid irritating his shin, before deciding to sit out Saturday's loss.
"As crazy as it sounds, I think it's good [that Bryant is sitting out]," Brown said following Monday's shootaround. "I'm more than OK with it. That's why you have 13-14 guys on your team.
"Now, obviously I would rather have Kobe than not -- get that clear -- but it's good for him to rest," Brown added. "It's good for him to take some time off and get his body right and get this injury right, especially at this point in the season."
The medical term for Bryant's injury is tenosynovitis, a condition where the tendon sheath in the shin has become inflamed. Bryant experiences irritation when his movement causes his tendon to slide in and out of the sheath.
Even with the improvement, there is no timetable for Bryant's return and his official status is day to day, according to the team.
Bryant, 33, leads the league in scoring at 28.1 points per game. He also is fourth in the league in minutes played per game (38.4).
The Lakers finish out their three-game road trip Wednesday in San Antonio, the first of three meetings in 10 days with the Southwest Division-leading Spurs.
"I'm taking it day by day and again, it ain't the end of the world if [Bryant] needs another game [to rest]," Brown said.
"Do I hope we get that third spot? Yes, hands down, you want that third spot, you want home-court advantage," Brown said before Monday night's games. "But, at the end of the day, there's a belief that I still have in this team that we can win on the road."
By winning Monday, the Lakers improved to 13-16 away from Staples Center this season.
"Put it this way, I'd rather [Bryant] be fresh going into the playoffs and us be fourth or fifth [in the Western Conference postseason standings] than him hurting or dinged up going into the playoffs and we're third," Brown said.
"I thought he played well for us," Brown said of Ebanks' surprise start Saturday, which came after he hadn't played more than 10 minutes in a game since Jan. 13 against Cleveland. "Especially not having played in as long as he hasn't played, I thought he came in and tried to do things the right way."