不知道你是否已经解决了这个问题，但是我也遇到了同样的问题。即使在next.js examples docs中有了最新的更新，它仍然给了我这个错误。所以我用谷歌搜索了一下，这样解决了这个问题：

const apolloServer = new ApolloServer({ typeDefs, resolvers });

const startServer = apolloServer.start();

export default async function handler(req, res) {
    res.setHeader("Access-Control-Allow-Credentials", "true");
    res.setHeader(
        "Access-Control-Allow-Origin",
        "https://studio.apollographql.com"
    );
    res.setHeader(
        "Access-Control-Allow-Headers",
        "Origin, X-Requested-With, Content-Type, Accept, Access-Control-Allow-Methods, Access-Control-Allow-Origin, Access-Control-Allow-Credentials, Access-Control-Allow-Headers"
    );
    res.setHeader(
        "Access-Control-Allow-Methods",
        "POST, GET, PUT, PATCH, DELETE, OPTIONS, HEAD"
    );
    if (req.method === "OPTIONS") {
        res.end();
        return false;
    }

    await startServer;
    await apolloServer.createHandler({
        path: "/api/graphql",
    })(req, res);
}

借助乔治Vlassis的回答，我在这里发布了阿波罗探索者工作所需的标题：

res.setHeader(
  'Access-Control-Allow-Origin',
  'https://studio.apollographql.com',
);
res.setHeader('Access-Control-Allow-Credentials', 'true');
res.setHeader('Access-Control-Allow-Headers', ' Content-Type');

如果您使用的是Apollo-server-Micro，那么您可以使用micro-cors：

yarn add micro-cors

然后，请记住导入micro_cors而不是micro-cors：

import micro_cors from "micro-cors"

const cors = micro_cors({
origin: "https://studio.apollographql.com",
allowCredentials:true,
allowMethods:["GET", "POST","PUT","DELETE"],
allowHeaders:["access-control-allow-credentials","access-control-allow-origin","content-type"]          
})

然后，用函数 Package ：

const handlers= cors(async  function  handlers(req: NextApiRequest, res:   NextApiResponse) {
await startServer

if (req.method === "OPTIONS") {
    res.end()
    return false
}

await apolloserver.createHandler({ path: "/api/graphql" })(req, res);
})

export default handlers

如果您通过以下方式诊断端点：

npx diagnose-endpoint@1.1.0 --endpoint=http://localhost:3000/api/graphql

并得到如下结果：

Diagnosing http://localhost:3000/api/graphql
⚠️  OPTIONS response is missing header 'access-control-allow-methods: POST'

只需将api.bodyParser设置为false，并将其作为一个配置常量放在graphql服务器API文件的底部，如下所示：

import type { NextApiRequest, NextApiResponse } from "next";
import { gql, ApolloServer } from "apollo-server-micro";
import { ApolloServerPluginLandingPageGraphQLPlayground } from "apollo-server-core";

...

const apolloServer = new ApolloServer({
    typeDefs,
    resolvers,
    plugins: [ApolloServerPluginLandingPageGraphQLPlayground()],
});

const startServer = apolloServer.start();

export default async function handler(
  req: NextApiRequest,
  res: NextApiResponse,
): Promise<void> {
  await startServer;
  await apolloServer.createHandler({
    path: "/api/graphql",
  })(req, res);
}

export const config = {
  api: {
    bodyParser: false,
  },
};

@yohanes Awnser差点就为我工作了！我不得不对它做一些修改：

import { ApolloServer } from 'apollo-server-micro';
import { applyMiddleware } from 'graphql-middleware';
import schema from '../../graphql/schema';
import { dataloadersMiddleware } from '../../graphql/loaders/middleware';
import microCors from "micro-cors";
import type { NextApiRequest, NextApiResponse } from 'next';
import { ApolloServerPluginLandingPageGraphQLPlayground } from 'apollo-server-core';
import { RequestHandler } from "micro";

const cors = microCors({ 
  allowMethods: [
    'Access-Control-Allow-Methods: *',
  ],
  allowHeaders: [
    'Access-Control-Allow-Origin: *',
  ],
  allowCredentials: true,
  origin: "*"
});

const server:ApolloServer = new ApolloServer({
  schema: applyMiddleware(schema, dataloadersMiddleware),
  playground: {
    endpoint: "/api/graphql",
  },
  persistedQueries: false,
  introspection: true,
  plugins: [ApolloServerPluginLandingPageGraphQLPlayground()]
} as any);

export const config = {
  api: {
    bodyParser: false,
  },
};

const startServer = server.start()

export default cors(async function handler(req: NextApiRequest, res: NextApiResponse):Promise<void> {
  await startServer;
  await server.createHandler({ path: "/api/graphql" })(req, res);
} as RequestHandler);