I don't think there is single response for this question, but I'll share my approach on how I'm currently doing Dependency Injection on Go with go-gin (but should be the nearly the same with any other router).
From a business point of view, I have a struct that wraps all access to my services which are responsible for business rules/processing.
// WchyContext is an application-wide context
type WchyContext struct {
    Health   services.HealthCheckService
    Tenant   services.TenantService
    ... whatever
}
My services are then just interfaces.
// HealthCheckService is a simple general purpose health check service
type HealthCheckService interface {
    IsDatabaseOnline() bool
}
Which have mulitple implementations, like MockedHealthCheck, PostgresHealthCheck, PostgresTenantService and so on.
My router than depends on a WchyContext, which the code looks like this:
func GetMainEngine(ctx context.WchyContext) *gin.Engine {
    router := gin.New()
    router.Use(gin.Logger())
    router.GET("/status", Status(ctx))
    router.GET("/tenants/:domain", TenantByDomain(ctx))
    return router
}`
Status and TenantByDomain act like a handler-factory, all it does is create a new handler based on given context, like this:
type statusHandler struct {
    ctx context.WchyContext
}
// Status creates a new Status HTTP handler
func Status(ctx context.WchyContext) gin.HandlerFunc {
    return statusHandler{ctx: ctx}.get()
}
func (h statusHandler) get() gin.HandlerFunc {
    return func(c *gin.Context) {
        c.JSON(200, gin.H{
            "healthy": gin.H{
                "database": h.ctx.Health.IsDatabaseOnline(),
            },
            "now":     time.Now().Format("2006.01.02.150405"),
        })
    }
}
As you can see, my health check handler doesn't care about concrete implementation of my services, I just use it whatever is in the ctx.
The last part depends on current execution environment. During automated tests I create a new WchyContext using mocked/stubbed services and send it to GetMainEngine, like this:
ctx := context.WchyContext{
    Health: &services.InMemoryHealthCheckService{Status: false},
    Tenant: &services.InMemoryTenantService{Tenants: []*models.Tenant{
        &models.Tenant{ID: 1, Name: "Orange Inc.", Domain: "orange"},
        &models.Tenant{ID: 2, Name: "The Triathlon Shop", Domain: "trishop"},
    }}
}
router := handlers.GetMainEngine(ctx)
request, _ := http.NewRequest(method, url, nil)
response := httptest.NewRecorder()
router.ServeHTTP(response, request)
... check if response matches what you expect from your handler
And when you setup it to really listen to a HTTP port, the wiring up looks like this: 
var ctx context.WchyContext
var db *sql.DB
func init() {
    db, _ = sql.Open("postgres", os.Getenv("DATABASE_URL"))
    ctx = context.WchyContext{
        Health: &services.PostgresHealthCheckService{DB: db},
        Tenant: &services.PostgresTenantService{DB: db}
    }
}
func main() {
    handlers.GetMainEngine(ctx).Run(":" + util.GetEnvOrDefault("PORT", "3000"))
}
There are a few things that I don't like about this, I'll probably refactor/improve it later, but it has been working well so far.
If you want to see full code reference, I'm working on this project here https://github.com/WeCanHearYou/wchy
Hope it can help you somehow.