It was not known what transpired at the brief meeting that took place in the Wankhede Stadium premises.
Shah had reached out to a sulking Shiv Sena Chief a day after the party announced its decision to boycott the ceremony on account of "constant humiliation" by BJP over government formation.
"Sena has missed the bus. I don't know due to whom," senior Sena leader and former Chief Minister Manohar Joshi said after the event.
Uddhav also shook hands and exchanged pleasantries with Prime Minister Narendra Modi after the proceedings got over but it was not yet clear if and when substantive talks between the two parties for thrashing out a mutually acceptable power-sharing arrangement will start.
"Sena is our natural ally. If they come with us, they are welcome. They have to take the call," senior BJP leader Om Prakash Mathur said.
Former Deputy Chief Minister Ajit Pawar, whose party NCP has declared unconditional outside support to the new government said, "We came here to wish the new CM our best. We will support the new government in all their pro-people decisions."