Bale wore the captain's armband for the first time in Wales' Nations League defeat against Denmark after Ashley Williams was rested last month.
Williams, 34, is expected to resume his captaincy duties when Wales face Spain next week but Giggs has backed Bale to skipper the nation.
"Going forward, definitely," Giggs said.
Bale is in the squad as Wales prepare to host Spain in an international friendly at the Principality Stadium on October 11 before facing the Republic of Ireland in the Nations League five days later.
"There's no pressure to play Gareth," said Giggs. "He had a little groin strain but the scan came back all clear and he expects to be involved at the weekend, which is good.
"With every player, you get the feedback of where they're at. We do a lot of work between camps logging the minutes certain players have played.
"We then try to get it right regarding training and game time, so we do as much homework as we can to see where the players are and to know what's best for the player and for us."
Giggs added: "It's not easy for Gareth. He's in the middle of the Champions League, so there's a midweek game, and at Real Madrid, you have to win every game.
"Every game is huge and it's just getting that balance right. How many minutes he plays, whether he misses a game and what's best for us and Real Madrid. Ideally, I want him to play every minute of every game."