Sock injured his hip when he took a fall during the first set of his men's singles clash.
After taking a 4-2 lead, the Japanese world No. 40 claimed the set in a tiebreaker.
The American took treatment during the break but then called it a day when trailing 7-6 (7-1) 1-1.
At one rubber apiece, the tie is drawn, with neither country capable of fielding their proper team for the deciding fast4 mixed doubles clash.
Vandeweghe will team up with her coach Pat Cash in an exhibition doubles clash, against Sugati and West Australian teenager Maddison Inglis.
Vandeweghe received a solid workout in her singles game despite the early withdrawal of her opponent.
The world No. 10 was put through her paces by 19-year-old Inglis, who has been used as a hitting partner during the tournament this summer and last.
Inglis, ranked 771 in the world, broke the serve of her more experienced opponent once in each set and with a bit of luck could have won the opening set.
But Vandeweghe delivered on important points to claim a 7-5 6-2 victory.
Vandeweghe admitted she has some work to do on the mental side of her game as the Australian Open gets nearer.
"I have been practising with Maddi all week, so she is comfortable with me and my game; I would think," she said.
"She is quite a different opponent to Naomi. But I'm just trying to do the best I can against any opponent who comes my way.
"It's more, for me, more a mental side, focusing on actual play. I got a bit sloppy out there, especially today.
"I think that's just the start of the season."
Despite her inexperience, Inglis showed plenty of promise at the start of 2016 when she won the Australian Open women's wildcard playoff against Arina Rodionova.
She returns to the game after having most of 2017 off.